A special class of nonstationary processes with periodically varying statistics, called cyclostationary (CS), is investigated. These processes are encountered in many engineering problems involving rotating machinery such as turbines, propellers, helicopter rotors, and diesel engines. We analyze a cyclostationary process model in order to show its advantages compared to a traditional stationary process model and present a methodology for calculating the statistics of the response of a linear system subjected to CS excitations. We demonstrate that a CS model estimates the statistics of the response of a linear dynamic system subjected to CS excitations more accurately by considering (1) a vehicle traveling on a rough road and (2) a propeller rotating in the wake of a ship in the presence of turbulence. In the case of the vehicle, the road consists of concrete plates of fixed length. We model the road excitation using a CS process and calculate the standard deviation (root mean square) of the vehicle response. In the case of the ship propeller, we calculate the hydrodynamic forces acting on the propeller using the vortex panel method and the vortex theory of propeller. Considering the randomness in the axial and the tangential components of velocity, we calculate the mean and the covariance of the forces. This analysis shows that the hydrodynamic forces acting on the propeller are CS processes. Then we perform finite element analysis of the propeller and calculate the mean and the standard deviation of the blade response. We do the parametric analysis to demonstrate the effects of some physical quantities such as the standard deviation, the correlation coefficient, the decorrelation time, and the scale of turbulence of the axial and the tangential components of the wake velocity on the standard deviation of the blade deflection. We found that the CS model yields the time-wise variation of the statistics of the excitation and the response (e.g., the root mean square) and their peaks correctly. This is important information for the calculation of probability of failure of the propeller. A traditional stationary model cannot provide this information. / Master of Science

The aim of this work is to evaluate ride quality of a typical passenger car. This requires both identifying the excitation resources, which result to undesired noise inside the vehicle, and studying human reaction t applied vibration. Driveline linear torsional vibration will be modelled by a 14-degress of freedom system while engine cylinder pressure torques are considered as an input force for the structure. The results show good agreement with the corresponding reference output responses which proves the accuracy of the numerical approach fourth order Runge-kutta. An eighteen-degree of freedom model is then used to investigate coupled motion of driveline and the tire/suspension assembly in order to attain vehicle body longitudinal acceleration subject to engine excitations. Road surface irregularities is simulated as a stationary random process and further vertical acceleration of the vehicle body will be obtained by considering the well-known quarter-car model including suspension/tire mechanisms and road input force. Finally, ISO diagrams are utilized to compare RMS vertical and lateral accelerations of the car body with the fatigue-decreased proficiency boundaries and to determine harmful frequency regions. According to the results, passive suspension system is not functional enough since its behaviour depends on frequency content of the input and it provides good isolation only when the car is subjected to a high frequency excitation. Although longitudinal RMS acceleration of the vehicle body due to engine force is not too significant, driveline torsional vibration itself has to be studied in order to avoid any dangerous damages for each component by recognizing resonance frequencies of the system. The report will come to an end by explaining different issues which are not investigated in this thesis and may be considered as future works.

Ground-borne vibration from underground rail vehicles is studied analytically. A previously developed model by J.A.Forrest and H.E.M.Hunt is modified to account for different track and vehicle models. The tunnel is modeled as infinite cylindrical shell surrounded by viscoelastic soil. The track is coupled to the tunnel with supports of complex stiffness. The rails, which are modeled as infinite Euler beams, are supported by discrete sleepers with regular spacing, and railpads with complex stiffness. A modified hysteretic damping model for moving loads is applied to soil. Linearized Hertzian contact spring is included between the wheel and the rail. The solution is obtained in frequency domain using random process theory. Effects of improvements in the model are graphically presented to enable comparison with the previously developed model and measurements from literature.

In the paper we study sequences of random functions which are defined by some interpolation procedures for a given random function. We investigate the problem in what sense and under which conditions the sequences converge to the prescribed random function. Sufficient conditions for convergence of moment characteristics, of finite dimensional distributions and for weak convergence of distributions in spaces of continuous functions are given. The treatment of such questions is stimulated by an investigation of Monte Carlo simulation procedures for certain classes of random functions. In an appendix basic facts concerning weak convergence of probability measures in metric spaces are summarized.

Neste trabalho de pesquisa desenvolveu-se uma metodologia, através de ensaios em túnel de vento, para determinar as cargas sobre estruturas altas situadas em centros urbanos e considerando a distribuição aleatória do entorno superficial. Assim, como este estudo trata do problema da determinação de cargas de estruturas situadas em centros urbanos, produziu-se, em primeiro lugar, o campo de velocidades de fundo, caracterizado por um terreno suburbano e definido pelo Código Brasileiro NBR/6123, Terreno Categoria IV. Posteriormente, nas cercanias do modelo em estudo, adicionou-se o entorno superficial. Para contemplar as variações das cargas provocadas pelo vento no entorno rugoso, as estruturas que o conformam dimensionaram-se através da Técnica Monte Carlo. Apresenta-se um método para reproduzir o entorno superficial em zonas centrais de grandes cidades, considerando a natureza aleatória das dimensões e a separação das construções, permitindo simular campos ou processos aleatórios, neste caso o entorno, definido como um campo aleatório tridimensional, em termos da densidade de probabilidade e da densidade espectral das construções. Analisou-se a estrutura da camada limite urbana na região inferior, por meio das medições em diferentes alturas das velocidades medias e flutuantes, intensidade de turbulência, macroescala integral e escala temporal da turbulência e espectros da componente de velocidade flutuante longitudinal. A bibliografia indica que para verificar a presença da subcamada rugosa, em camada limite sobre superfície rugosa, é suficiente comprovar que as tensões de Reynolds aumentam com a altura de medição. Neste trabalho, sem haver realizado medições de Tensões de Reynolds, foi possível reconhecer a presença da subcamada rugosa através de medições e comparações em diferentes alturas de velocidades médias e valores estatísticos da componente flutuante longitudinal do escoamento médio. Verificou-se que o campo de velocidade em centro urbano é nitidamente tridimensional e que a direção do vento de fundo influi no campo de velocidade. Ademais, sugeriu-se um espectro de potência para análise dinâmica de edifícios altos expostos à ação do vento em ambientes urbanos, assim como recomendações referidas à variação de velocidade e intensidade de turbulência da componente longitudinal da turbulência. Para analisar a confiabilidade das cargas de vento sugeridas nos códigos de vento Argentino e Brasilero estudaram-se as cargas sobre dois modelos de diferentes alturas, medidas em condição de modelo isolado e situado em seis situações de entornos rugosos diferentes. As cargas medidas foram momentos de flexão na base longitudinal e transversal ao escoamento médio e momento de torção. Com os resultados obtidos, pode-se avaliar as diferenças com respeito às cargas sugeridas pelos códigos NBR 6123 e CIRSOC 102 e as variações provocadas ao modificar as rugosidades superficiais. / In this research work a methodology to determine loads on tall structures located in urban centres is proposed. The proposal is based in wind tunnel tests and considers a random distribution of the surface environment. As this study deals with the determination of wind loads on structures located in urban centres, firstly the background wind velocity field, characterized by a suburban terrain, which is defined by the Brazilian code of practice NBR/6123 as a terrain of Category IV, had to be reproduced. Thereafter, the near environment of the model under study was added. In order to take into account the variations of loads caused by the random environment, the structures that shape it were dimensioned using the Monte Carlo technique. A procedure to reproduce the surface neighbouring in central areas of large cities considering the random nature of both size and distribution of buildings is presented. This procedure allows simulating either random fields or processes, in this case the neighbouring, which is defined as a three-dimensional random field, in terms of both its probability density and its spectral density. The structure of the lower part of the urban boundary layer was studied by means of measurements at different heights of both fluctuating and mean velocities, turbulence intensity, integral macroscale and time scale of turbulence, and spectra of the longitudinal fluctuating velocity component. It is widely accepted in the literature that verifying that the Reynold stresses increases with height is sufficient to prove the existence of the rough sublayer in a boundary layer over rough surface. As in this work Reynolds stresses were not measured, it was possible to distinguish the presence of a roughness surface through measurements and comparisons of mean velocities and statistical values of the longitudinal fluctuating component of the mean flow at different heights. It was verified that the velocity field in an urban centre is clearly three-dimensional and that the direction of the background wind has influence on the velocity field. Furthermore, a power spectrum for the dynamic analysis of tall buildings exposed to wind in urban environments is suggested as well as guidelines regarding the variation of both the velocity and turbulence intensity of the longitudinal component of the turbulence. Loads over two models were studied in order to analyse the reliability of the loads suggested by codes of Argentina e Brasilero. The models had different heights and loads were measured with the models isolated and in six situations of different rough urban environments. The loads that were measured were longitudinal-to-the-mean-flow and transversal-to-themean- flow bending and torsion moments. With these results it was possible to assess the differences with regard to loads suggested by the code NBR 6123 and CIRSOC 102 and the variations appearing when changing the surface roughness.

Neste trabalho de pesquisa desenvolveu-se uma metodologia, através de ensaios em túnel de vento, para determinar as cargas sobre estruturas altas situadas em centros urbanos e considerando a distribuição aleatória do entorno superficial. Assim, como este estudo trata do problema da determinação de cargas de estruturas situadas em centros urbanos, produziu-se, em primeiro lugar, o campo de velocidades de fundo, caracterizado por um terreno suburbano e definido pelo Código Brasileiro NBR/6123, Terreno Categoria IV. Posteriormente, nas cercanias do modelo em estudo, adicionou-se o entorno superficial. Para contemplar as variações das cargas provocadas pelo vento no entorno rugoso, as estruturas que o conformam dimensionaram-se através da Técnica Monte Carlo. Apresenta-se um método para reproduzir o entorno superficial em zonas centrais de grandes cidades, considerando a natureza aleatória das dimensões e a separação das construções, permitindo simular campos ou processos aleatórios, neste caso o entorno, definido como um campo aleatório tridimensional, em termos da densidade de probabilidade e da densidade espectral das construções. Analisou-se a estrutura da camada limite urbana na região inferior, por meio das medições em diferentes alturas das velocidades medias e flutuantes, intensidade de turbulência, macroescala integral e escala temporal da turbulência e espectros da componente de velocidade flutuante longitudinal. A bibliografia indica que para verificar a presença da subcamada rugosa, em camada limite sobre superfície rugosa, é suficiente comprovar que as tensões de Reynolds aumentam com a altura de medição. Neste trabalho, sem haver realizado medições de Tensões de Reynolds, foi possível reconhecer a presença da subcamada rugosa através de medições e comparações em diferentes alturas de velocidades médias e valores estatísticos da componente flutuante longitudinal do escoamento médio. Verificou-se que o campo de velocidade em centro urbano é nitidamente tridimensional e que a direção do vento de fundo influi no campo de velocidade. Ademais, sugeriu-se um espectro de potência para análise dinâmica de edifícios altos expostos à ação do vento em ambientes urbanos, assim como recomendações referidas à variação de velocidade e intensidade de turbulência da componente longitudinal da turbulência. Para analisar a confiabilidade das cargas de vento sugeridas nos códigos de vento Argentino e Brasilero estudaram-se as cargas sobre dois modelos de diferentes alturas, medidas em condição de modelo isolado e situado em seis situações de entornos rugosos diferentes. As cargas medidas foram momentos de flexão na base longitudinal e transversal ao escoamento médio e momento de torção. Com os resultados obtidos, pode-se avaliar as diferenças com respeito às cargas sugeridas pelos códigos NBR 6123 e CIRSOC 102 e as variações provocadas ao modificar as rugosidades superficiais. / In this research work a methodology to determine loads on tall structures located in urban centres is proposed. The proposal is based in wind tunnel tests and considers a random distribution of the surface environment. As this study deals with the determination of wind loads on structures located in urban centres, firstly the background wind velocity field, characterized by a suburban terrain, which is defined by the Brazilian code of practice NBR/6123 as a terrain of Category IV, had to be reproduced. Thereafter, the near environment of the model under study was added. In order to take into account the variations of loads caused by the random environment, the structures that shape it were dimensioned using the Monte Carlo technique. A procedure to reproduce the surface neighbouring in central areas of large cities considering the random nature of both size and distribution of buildings is presented. This procedure allows simulating either random fields or processes, in this case the neighbouring, which is defined as a three-dimensional random field, in terms of both its probability density and its spectral density. The structure of the lower part of the urban boundary layer was studied by means of measurements at different heights of both fluctuating and mean velocities, turbulence intensity, integral macroscale and time scale of turbulence, and spectra of the longitudinal fluctuating velocity component. It is widely accepted in the literature that verifying that the Reynold stresses increases with height is sufficient to prove the existence of the rough sublayer in a boundary layer over rough surface. As in this work Reynolds stresses were not measured, it was possible to distinguish the presence of a roughness surface through measurements and comparisons of mean velocities and statistical values of the longitudinal fluctuating component of the mean flow at different heights. It was verified that the velocity field in an urban centre is clearly three-dimensional and that the direction of the background wind has influence on the velocity field. Furthermore, a power spectrum for the dynamic analysis of tall buildings exposed to wind in urban environments is suggested as well as guidelines regarding the variation of both the velocity and turbulence intensity of the longitudinal component of the turbulence. Loads over two models were studied in order to analyse the reliability of the loads suggested by codes of Argentina e Brasilero. The models had different heights and loads were measured with the models isolated and in six situations of different rough urban environments. The loads that were measured were longitudinal-to-the-mean-flow and transversal-to-themean- flow bending and torsion moments. With these results it was possible to assess the differences with regard to loads suggested by the code NBR 6123 and CIRSOC 102 and the variations appearing when changing the surface roughness.

Made available in DSpace on 2014-06-11T19:22:26Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-01-29Bitstream added on 2014-06-13T18:49:05Z : No. of bitstreams: 1 marques_ha_me_prud.pdf: 1098327 bytes, checksum: 37aabdd60dc21333c03db5177953ea93 (MD5) / Dados de receptores GPS de dupla freqüência são, em geral, processados utilizando a combinação ion-free, o que permite eliminar os efeitos de primeira ordem da ionosfera. Porém, os efeitos de segunda e terceira ordem, geralmente, são negligenciados no processamento de dados GPS. Nesse trabalho, esses efeitos foram levados em consideração no processamento dos dados. Foram investigados os modelos matemáticos associados a esses efeitos, as transformações envolvendo o campo magnético da Terra e a utilização do TEC advindo dos Mapas Globais da Ionosfera ou calculados a partir das pseudodistâncias. Numa outra investigação independente, os efeitos residuais de primeira ordem da ionosfera, resultantes da dupla diferença da pseudodistância e da fase da onda portadora, foram considerados como incógnitas no ajustamento. Porém, esses efeitos residuais foram tratados como pseudo-observações, associados aos processos aleatórios random walk e white noise e, adicionados ao algoritmo de filtro de Kalman. Dessa forma, o modelo matemático preserva a característica de número inteiro da ambigüidade da fase, facilitando a aplicação de algoritmos de solução da ambigüidade, que no caso desse trabalho, utilizou-se o método LAMBDA. Para o caso da consideração dos efeitos de segunda e terceira ordem da ionosfera, foram realizados processamentos de dados GPS envolvendo o modo relativo e o Posicionamento por Ponto Preciso. Os resultados mostraram que a não consideração desses efeitos no processamento dos dados GPS pode introduzir variações da ordem de três a quatro milímetros nas coordenadas das estações. / Data from dual frequency receiver, in general, are processed using the ion-free combination that allows the elimination of the first order ionospheric effects. However, the second and third order ionospheric effects, generally, are neglected in the GPS data processing. In this work, these effects were taken into account in the GPS data processing. In this case, it was investigated the mathematical models associated with the second and third order effects, the transformations involving the Earth magnetic field and the use of TEC from Ionosphere Global Maps or calculated from the pseudoranges. The first order ionosphere residual effects, resulting from pseudorange and phase double difference, were taken into account as unknown in the adjustment. However, these effects were treated as pseudo-observables and it was associated with the random process random walk and white noise and added to the Kalman filter algorithm. Therefore, the mathematical model preserves the phase ambiguity “integerness”, facilitating the application of ambiguity resolution approaches, which in the case of this work, it was used the LAMBDA method.

Neste trabalho de pesquisa desenvolveu-se uma metodologia, através de ensaios em túnel de vento, para determinar as cargas sobre estruturas altas situadas em centros urbanos e considerando a distribuição aleatória do entorno superficial. Assim, como este estudo trata do problema da determinação de cargas de estruturas situadas em centros urbanos, produziu-se, em primeiro lugar, o campo de velocidades de fundo, caracterizado por um terreno suburbano e definido pelo Código Brasileiro NBR/6123, Terreno Categoria IV. Posteriormente, nas cercanias do modelo em estudo, adicionou-se o entorno superficial. Para contemplar as variações das cargas provocadas pelo vento no entorno rugoso, as estruturas que o conformam dimensionaram-se através da Técnica Monte Carlo. Apresenta-se um método para reproduzir o entorno superficial em zonas centrais de grandes cidades, considerando a natureza aleatória das dimensões e a separação das construções, permitindo simular campos ou processos aleatórios, neste caso o entorno, definido como um campo aleatório tridimensional, em termos da densidade de probabilidade e da densidade espectral das construções. Analisou-se a estrutura da camada limite urbana na região inferior, por meio das medições em diferentes alturas das velocidades medias e flutuantes, intensidade de turbulência, macroescala integral e escala temporal da turbulência e espectros da componente de velocidade flutuante longitudinal. A bibliografia indica que para verificar a presença da subcamada rugosa, em camada limite sobre superfície rugosa, é suficiente comprovar que as tensões de Reynolds aumentam com a altura de medição. Neste trabalho, sem haver realizado medições de Tensões de Reynolds, foi possível reconhecer a presença da subcamada rugosa através de medições e comparações em diferentes alturas de velocidades médias e valores estatísticos da componente flutuante longitudinal do escoamento médio. Verificou-se que o campo de velocidade em centro urbano é nitidamente tridimensional e que a direção do vento de fundo influi no campo de velocidade. Ademais, sugeriu-se um espectro de potência para análise dinâmica de edifícios altos expostos à ação do vento em ambientes urbanos, assim como recomendações referidas à variação de velocidade e intensidade de turbulência da componente longitudinal da turbulência. Para analisar a confiabilidade das cargas de vento sugeridas nos códigos de vento Argentino e Brasilero estudaram-se as cargas sobre dois modelos de diferentes alturas, medidas em condição de modelo isolado e situado em seis situações de entornos rugosos diferentes. As cargas medidas foram momentos de flexão na base longitudinal e transversal ao escoamento médio e momento de torção. Com os resultados obtidos, pode-se avaliar as diferenças com respeito às cargas sugeridas pelos códigos NBR 6123 e CIRSOC 102 e as variações provocadas ao modificar as rugosidades superficiais. / In this research work a methodology to determine loads on tall structures located in urban centres is proposed. The proposal is based in wind tunnel tests and considers a random distribution of the surface environment. As this study deals with the determination of wind loads on structures located in urban centres, firstly the background wind velocity field, characterized by a suburban terrain, which is defined by the Brazilian code of practice NBR/6123 as a terrain of Category IV, had to be reproduced. Thereafter, the near environment of the model under study was added. In order to take into account the variations of loads caused by the random environment, the structures that shape it were dimensioned using the Monte Carlo technique. A procedure to reproduce the surface neighbouring in central areas of large cities considering the random nature of both size and distribution of buildings is presented. This procedure allows simulating either random fields or processes, in this case the neighbouring, which is defined as a three-dimensional random field, in terms of both its probability density and its spectral density. The structure of the lower part of the urban boundary layer was studied by means of measurements at different heights of both fluctuating and mean velocities, turbulence intensity, integral macroscale and time scale of turbulence, and spectra of the longitudinal fluctuating velocity component. It is widely accepted in the literature that verifying that the Reynold stresses increases with height is sufficient to prove the existence of the rough sublayer in a boundary layer over rough surface. As in this work Reynolds stresses were not measured, it was possible to distinguish the presence of a roughness surface through measurements and comparisons of mean velocities and statistical values of the longitudinal fluctuating component of the mean flow at different heights. It was verified that the velocity field in an urban centre is clearly three-dimensional and that the direction of the background wind has influence on the velocity field. Furthermore, a power spectrum for the dynamic analysis of tall buildings exposed to wind in urban environments is suggested as well as guidelines regarding the variation of both the velocity and turbulence intensity of the longitudinal component of the turbulence. Loads over two models were studied in order to analyse the reliability of the loads suggested by codes of Argentina e Brasilero. The models had different heights and loads were measured with the models isolated and in six situations of different rough urban environments. The loads that were measured were longitudinal-to-the-mean-flow and transversal-to-themean- flow bending and torsion moments. With these results it was possible to assess the differences with regard to loads suggested by the code NBR 6123 and CIRSOC 102 and the variations appearing when changing the surface roughness.

Aggregated data appears in many areas such as econimics, sociology, geography, etc. This motivates an importance of studying the (dis)aggregation problem. One of the most important reasons why the contemporaneous aggregation become an object of research is the possibility of obtaining the long memory phenomena in processes. The aggregation provides an explanation of the long-memory effect in time series and a simulation method of such series as well. Accumulation of short-memory non-ergodic random processes can lead to the long memory ergodic process, that can be used for the forecasts of the macro and micro variables. We explore the aggregation scheme of AR(1) processes and nearest-neighbour random fields with infinite variance. We provide results on the existence of limit aggregated processes, and find conditions under which it has long memory properties in certain sense. For the random fields on Z^2, we introduce the notion of (an)isotropic long memory based on the behavior of partial sums. In L_2 case, the known aggregation of independent AR(1) processes leads to the Gaussian limit. While we describe a new model of aggregation based on independent triangular arrays. This scheme gives the limit aggregated process with finite variance which is not necessary Gaussian. We study a discrete time risk insurance model with stationary claims, modeled by the aggregated heavy-tailed process. We establish the asymptotic properties of the ruin probability and the dependence structure... [to full text] / Agreguoti duomenys naudojami daugelyje mokslo sričių tokių kaip ekonomika, sociologija, geografija ir kt. Tai motyvuoja tirti (de)agregavimo uždavinį. Viena iš pagrindinių priežasčių kodėl vienalaikis agregavimas tapo tyrimų objektu yra galimybė gauti ilgos atminties procesus. Agregavimas paaiškina ilgos atminties atsiradima procesuose ir yra vienas iš būdų tokius procesus generuoti. Agreguodami trumpos atminties neergodiškus atsitiktinius procesus, galime gauti ilgos atminties ergodišką procesą, kuris gali būti naudojamas mikro ir makro kintamųjų prognozavimui. Disertacijoje nagrinėjama AR(1) procesų bei artimiausio kaimyno atsitiktinių laukų, turinčių begalinę dispersiją, agregavimo schema, randamos sąlygos, kurioms esant ribinis agreguotas procesas egzistuoja, ir turi ilgąją atmintį tam tikra prasme. Atsitiktinių laukų atveju, įvedamas anizotropinės/izotropinės ilgos atminties apibrėžimas, kuris yra paremtas dalinių sumų elgesiu. Baigtinės dispersijos atveju yra gerai žinoma nepriklausomų AR(1) procesų schema, kuri rezultate duoda Gauso ribinį agreguotą procesą. Disertacijoje aprašoma trikampio masyvo agregavimo modelis, kuris baigtinės dispersijos atveju duoda nebūtinai Gauso ribinį agreguotą procesą. Taip pat disertacijoje nagrinėjama bankroto tikimybės asimptotika, kai žalos yra aprašomos sunkiauodegiu agreguotu procesu, nusakoma priklausomybė tarp žalų, apibūdinama žalų ilga atmintis.

Agreguoti duomenys naudojami daugelyje mokslo sričių tokių kaip ekonomika, sociologija, geografija ir kt. Tai motyvuoja tirti (de)agregavimo uždavinį. Viena iš pagrindinių priežasčių kodėl vienalaikis agregavimas tapo tyrimų objektu yra galimybė gauti ilgos atminties procesus. Agregavimas paaiškina ilgos atminties atsiradima procesuose ir yra vienas iš būdų tokius procesus generuoti. Agreguodami trumpos atminties neergodiškus atsitiktinius procesus, galime gauti ilgos atminties ergodišką procesą, kuris gali būti naudojamas mikro ir makro kintamųjų prognozavimui. Disertacijoje nagrinėjama AR(1) procesų bei artimiausio kaimyno atsitiktinių laukų, turinčių begalinę dispersiją, agregavimo schema, randamos sąlygos, kurioms esant ribinis agreguotas procesas egzistuoja, ir turi ilgąją atmintį tam tikra prasme. Atsitiktinių laukų atveju, įvedamas anizotropinės/izotropinės ilgos atminties apibrėžimas, kuris yra paremtas dalinių sumų elgesiu. Baigtinės dispersijos atveju yra gerai žinoma nepriklausomų AR(1) procesų schema, kuri rezultate duoda Gauso ribinį agreguotą procesą. Disertacijoje aprašoma trikampio masyvo agregavimo modelis, kuris baigtinės dispersijos atveju duoda nebūtinai Gauso ribinį agreguotą procesą. Taip pat disertacijoje nagrinėjama bankroto tikimybės asimptotika, kai žalos yra aprašomos sunkiauodegiu agreguotu procesu, nusakoma priklausomybė tarp žalų, apibūdinama žalų ilga atmintis. / Aggregated data appears in many areas such as econimics, sociology, geography, etc. This motivates an importance of studying the (dis)aggregation problem. One of the most important reasons why the contemporaneous aggregation become an object of research is the possibility of obtaining the long memory phenomena in processes. The aggregation provides an explanation of the long-memory effect in time series and a simulation method of such series as well. Accumulation of short-memory non-ergodic random processes can lead to the long memory ergodic process, that can be used for the forecasts of the macro and micro variables. We explore the aggregation scheme of AR(1) processes and nearest-neighbour random fields with infinite variance. We provide results on the existence of limit aggregated processes, and find conditions under which it has long memory properties in certain sense. For the random fields on Z^2, we introduce the notion of (an)isotropic long memory based on the behavior of partial sums. In L_2 case, the known aggregation of independent AR(1) processes leads to the Gaussian limit. While we describe a new model of aggregation based on independent triangular arrays. This scheme gives the limit aggregated process with finite variance which is not necessary Gaussian. We study a discrete time risk insurance model with stationary claims, modeled by the aggregated heavy-tailed process. We establish the asymptotic properties of the ruin probability and the dependence structure... [to full text]