Nesta dissertação de mestrado, vamos apresentar uma prova para os grandes desvios para variáveis aleatórias independentes e identicamente distribuídas com todos os momentos finitos e para a medida empírica de cadeias de Markov com espaço de estados finito e tempo discreto. Além disso, abordaremos os teoremas de Sanov e Gärtner-Ellis. / In this master thesis it is presented a proof of the large deviations for independent and identically distributed random variables with all finite moments and for the empirical measure of Markov chains with finite state space and with discrete time. Moreover, we address the theorems of Sanov and of Gartner-Ellis.

Submitted by DIEGO FERNANDO LAMBER MARTINS CANO null (diegolamber4@hotmail.com) on 2016-07-02T10:48:20Z No. of bitstreams: 1 Dissertação - Diego Cano - Revisão III.docx: 189771 bytes, checksum: 9a1f5f988aa18f362b529fbcfa16f650 (MD5) / Rejected by Ana Paula Grisoto (grisotoana@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: A versão final da dissertação/tese deve ser submetida no formato PDF (Portable Document Format). O arquivo PDF não deve estar protegido e a dissertação/tese deve estar em um único arquivo, inclusive os apêndices e anexos, se houver. Por favor, corrija o formato do arquivo e realize uma nova submissão. Agradecemos a compreensão. on 2016-07-06T18:01:28Z (GMT) / Submitted by DIEGO FERNANDO LAMBER MARTINS CANO null (diegolamber4@hotmail.com) on 2016-07-06T23:46:26Z No. of bitstreams: 1 Dissertação - Diego Cano - Revisão III.pdf: 364171 bytes, checksum: 50db327642b399814ffc7d03be0145dd (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-07-07T12:31:00Z (GMT) No. of bitstreams: 1 cano_dflm_me_bot.pdf: 364171 bytes, checksum: 50db327642b399814ffc7d03be0145dd (MD5) / Made available in DSpace on 2016-07-07T12:31:00Z (GMT). No. of bitstreams: 1 cano_dflm_me_bot.pdf: 364171 bytes, checksum: 50db327642b399814ffc7d03be0145dd (MD5) Previous issue date: 2016-05-04 / Em decorrência de processo fisiológico natural, mulheres menopausadas estão expostas a diminuição da massa muscular devido à redução dos níveis hormonais. Consequentemente, podem ocorrer alterações posturais. Adicionalmente, as alterações posturais estão relacionadas aos maus hábitos da postura, sedentarismo e obesidade. Com o objetivo de associar as alterações posturais com indicadores demográficos, socioeconômicos, antropométricos e aptidão física de mulheres menopausadas, foram analisados dados de 317 mulheres, no momento inicial das avaliações, nos anos de 2013 e 2014, participantes no programa de mudança do estilo de vida (Mexa-se Pró Saúde) da cidade de Botucatu/SP. Foram analisados os seguintes desvios posturais: protusão cervical, cifose torácica, lordose lombar, ângulos quadricipitais direito e esquerdo. Adotou-se o teste do qui quadrado para associação entre os desvios posturais e as variáveis demográficas, IMC e de aptidão física. Foi realizada a regressão logística considerando as demais variáveis como explanatórias. O nível de significância adotado foi de 5%. Na amostra, 62,8% eram abaixo de sessenta anos, maioria casada (63,1%), de nível médio de escolaridade (56,5%), vivendo com renda familiar inferior a 5 salários mínimos (76,3%). Cerca de metade das mulheres apresentava desvios posturais (para mais ou para menos) de protusão, cifose e lordose, enquanto essas distorções aumentaram ainda mais para os ângulos quadricipitais direito e esquerdo. Na análise logística das alterações posturais aumentadas, constituíram alterações para a protusão a idade superior a 60 anos (OR 2,07; 1,33-3,24) e para cifose, o nível baixo de atividade física (OR 2,46; 1,26-4,80). Não houve influência significativa do excesso de peso nas alterações posturais analisadas. Conclui-se que, embora com desvios posturais frequentes e com fatores de risco já conhecidos, essas mulheres estão aptas aos modelos de estilo de vida saudável, com exercícios físicos supervisionados. / Resulting from a natural physiological process, women after menopause are open to a decrease of muscular mass because of the reduction of hormone levels. Consequently, postural alterations can happen. Additionally, these postural alterations are related to bad postural habits, sedentarism and obesity. With the objective to associate postural alterations with demographical indicators, social-economics, anthropometry and physical aptitude, data from 317 post-menopause women were analyzed. The initial evaluations made in 2013 and 2014 were from women participating in the program to change their life style (Mexa-se Pró-Saúde) in the city of Botucatu, S.P. The following postural deviations were analyzed: cervical protrusion, thoraxical kyphosis, lumbar lordosis, and the right and left quadriceps angles. The qui quadratic test was used for association between postural deviations and demographical variables, Index of Physical Mass, and physical aptitude. There was a logistic regression made to consider as explanatory all other variables. The significance level adopted was 5%. In our example, 62.8% were under 60 years of age, 63.1% were married, 56.5% had a medium school level, 76.3% lived with a family income of less than five minimum salaries. Almost half the women presented postural deviations (some more, some less) of cervical protrusion, kyphosis and lordosis, while these distortions increased more for right and left quadriceps angles. In the logistical analysis of increased postural alterations, there was a risk factor constituted for protrusion to an age higher than 60 years old (OR2.07; 1,33-3,24) and for kyphosis a low level of physical activity (OR2,46; 1,26- 4,80). There was no significant influence observed in ´postural alterations related to overweight. In conclusion, even though postural alterations are frequent and have known risk factors, these women are apt as models of healthy life styles, with supervised physical exercises.

Orientador: Roberto Carlos Burini / Resumo: Em decorrência de processo fisiológico natural, mulheres menopausadas estão expostas a diminuição da massa muscular devido à redução dos níveis hormonais. Consequentemente, podem ocorrer alterações posturais. Adicionalmente, as alterações posturais estão relacionadas aos maus hábitos da postura, sedentarismo e obesidade. Com o objetivo de associar as alterações posturais com indicadores demográficos, socioeconômicos, antropométricos e aptidão física de mulheres menopausadas, foram analisados dados de 317 mulheres, no momento inicial das avaliações, nos anos de 2013 e 2014, participantes no programa de mudança do estilo de vida (Mexa-se Pró Saúde) da cidade de Botucatu/SP. Foram analisados os seguintes desvios posturais: protusão cervical, cifose torácica, lordose lombar, ângulos quadricipitais direito e esquerdo. Adotou-se o teste do qui quadrado para associação entre os desvios posturais e as variáveis demográficas, IMC e de aptidão física. Foi realizada a regressão logística considerando as demais variáveis como explanatórias. O nível de significância adotado foi de 5%. Na amostra, 62,8% eram abaixo de sessenta anos, maioria casada (63,1%), de nível médio de escolaridade (56,5%), vivendo com renda familiar inferior a 5 salários mínimos (76,3%). Cerca de metade das mulheres apresentava desvios posturais (para mais ou para menos) de protusão, cifose e lordose, enquanto essas distorções aumentaram ainda mais para os ângulos quadricipitais direito e esquerdo. Na análise logísti... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Resulting from a natural physiological process, women after menopause are open to a decrease of muscular mass because of the reduction of hormone levels. Consequently, postural alterations can happen. Additionally, these postural alterations are related to bad postural habits, sedentarism and obesity. With the objective to associate postural alterations with demographical indicators, social-economics, anthropometry and physical aptitude, data from 317 post-menopause women were analyzed. The initial evaluations made in 2013 and 2014 were from women participating in the program to change their life style (Mexa-se Pró-Saúde) in the city of Botucatu, S.P. The following postural deviations were analyzed: cervical protrusion, thoraxical kyphosis, lumbar lordosis, and the right and left quadriceps angles. The qui quadratic test was used for association between postural deviations and demographical variables, Index of Physical Mass, and physical aptitude. There was a logistic regression made to consider as explanatory all other variables. The significance level adopted was 5%. In our example, 62.8% were under 60 years of age, 63.1% were married, 56.5% had a medium school level, 76.3% lived with a family income of less than five minimum salaries. Almost half the women presented postural deviations (some more, some less) of cervical protrusion, kyphosis and lordosis, while these distortions increased more for right and left quadriceps angles. In the logistical analysis of increased pos... (Complete abstract click electronic access below) / Mestre

Nesta dissertação de mestrado, vamos apresentar uma prova para os grandes desvios para variáveis aleatórias independentes e identicamente distribuídas com todos os momentos finitos e para a medida empírica de cadeias de Markov com espaço de estados finito e tempo discreto. Além disso, abordaremos os teoremas de Sanov e Gärtner-Ellis. / In this master thesis it is presented a proof of the large deviations for independent and identically distributed random variables with all finite moments and for the empirical measure of Markov chains with finite state space and with discrete time. Moreover, we address the theorems of Sanov and of Gartner-Ellis.

The objective of this thesis is to check the preciseness of the total station Leica TC(R) 407 ser. No.660021 by using the defined methods. The data collected through measurements and by the computation procedures according to the relevant standards and the proceedings described by the professional literature were compared with the data stated by the manufacturer. The accuracy of the telemeter and the goniometric part of the device was tested. The theoretical part of this thesis is focused on the basic measurement methods and distance determination, principle of the electronic direction measuring and the error theory. The practical part of the thesis is focused on checking the accuracy of the measured horizontal direction and the zenith angle, as well as checking the preciseness of the telemetric part of the device. As a result the standard deviations of the measured distances and directions have been determined.

Orientador: Miguel Natálio Abadi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T15:39:00Z (GMT). No. of bitstreams: 1 Lambert_Rodrigo_M.pdf: 3549677 bytes, checksum: 663438e1feb8f7092723382b6846bc9c (MD5) Previous issue date: 2010 / Resumo: Seja x um alfabeto finito ou enumerável, e considere o espaço de todas as sequências finitas compostas por concatenação de símbolos desse alfabeto. A essas sequências daremos o nome de palavras. Denotaremos por xn conjunto de todas as palavras de tamanho n. No presente trabalho, consideramos uma função que leva cada palavra de tamanho n em um número inteiro entre 0 e n - 1. Essa função é definida pelo maior tamanho possível de uma sobreposição da palavra com uma cópia dela mesma transladada, e é chamada de função de sobreposição. A ela daremos o nome de Sn. A relevância da função de sobreposição foi colocada em evidência, entre outros casos, na análise estatística da Recorrência de Poincaré, e possui relação explícita com a entropia do processo. Nesse trabalho, provamos a convergência da distribuição da função de sobreposição, quando a sequência _e escolhida de acordo com relação a n variáveis aleatórias independentes e identicamente distribuídas no alfabeto x. Também apresentamos um limitante para a velocidade dessa convergência. Como consequência, mostramos também a convergência da esperança e da variância da função de sobreposição. / Abstract: We consider the set of finite sequencies of length n over a finite or contable alphabet x. We consider the function defined over xn which gives the size of the maximum overlap of a given sequence with a (shifted) copy of itself. That function will be denoted by overlapping function. We prove the convergence of the distribution of this function when the sequence is chosen according to a product measure, with identically distributed marginals. We give a point-wise upper bound for the velocity of this convergence. As a byproduct, we show the convergence of te mean and the variance of the overlapping function. / Mestrado / Probabilidade / Mestre em Estatística

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L’objet de cette thèse concerne l’étude asymptotique des processus de branchement sur-critiques en environnement aléatoire, qui sont une généralisation du processus de Galton-Watson, avec une loi de reproduction choisie aléatoirement et de manière i.i.d. suivant les générations. Dans le cas de non extinction, nous démontrons une succession de résultats asymptotiques plus fins que ceux établis dans des travaux antérieurs. Le chapitre 1 est consacré à l’étude de l’écart relatif entre le processus (Zn) normalisé et la loi normale. Nous établissons une borne de type Berry-Esseen ainsi qu’un développement pour des déviations de type Cramér, généralisant ainsi le théorème central limite et le principe des déviations modérées établis précédemment dans la littérature. Le second chapitre concerne l'asymptotique de la distribution du processus (Zn) ainsi que le moment harmonique critique de la variable limite W de la population normalisée. Nous établissons un équivalent de l'asymptotique de la distribution du processus Zn et donnons une caractérisation des constantes via une équation fonctionnelle similaire au cas du processus de Galton-Watson. Dans le cas des processus de branchement en environnement aléatoire, les résultats améliorent l'équivalent asymptotique de la distribution de Zn établi dans des travaux antérieurs sous normalisation logarithmique, sous la condition que chaque individu donne naissance à au moins un individu. Nous déterminons aussi la valeur critique pour l'existence du moment harmonique de W sous des conditions simples d'existence de moments, qui sont bien plus faibles que les hypothèses imposées dans la littérature, et généralisons le résultat à Z_0=k individus initiaux. Le troisième chapitre est consacré à l'étude de l'asymptotique des moments harmoniques d'ordre r>0 de Zn. Nous établissons un équivalent et donnons une expression des constantes. Le résultat met en évidence un phénomène de transition de phase, relié aux transitions de phase des grandes déviations inférieures du processus (Zn). En application de ce résultat, nous établissons un résultat de grandes déviations inférieures pour le processus (Zn) sous des hypothèses plus faibles que celles imposées dans des travaux précédents. Nous améliorons également la vitesse de convergence dans un théorème central limite vérifié par W_n-W, et déterminons l'asymptotique de la probabilité de grandes déviations pour le ratio Zn+1/Z_n. / The purpose of this Ph.D. thesis is the study of branching processes in a random environment, say (Z_n), which are a generalization of the Galton-Watson process, with the reproduction law chosen randomly in each generation in an i.i.d. manner. We consider the case of a supercritical process, assuming the condition that each individual gives birth to at least one child. The first part of this work is devoted to the study of the relative and absolute distance between the normalized process log Z_n and the normal law. We show a Berry-Esseen bound and establish a Cramér type large deviation expansion, which generalize the central limit theorem and the moderate deviation principle established for log Z_n in previous studies.In the second chapter we study the asymptotic of the distribution of Z_n, and the critical value for the existence of harmonic moments of the limit variable W of the normalized population size. We give an equivalent of the asymptotic distribution of Z_n and characterize the constants by a functional relation which is similar to that obtained for a Galton-Watson process. For a branching process in a random environment, our result generalizes the equivalent of the asymptotic distribution of Z_n established in a previous work in a log-scale, under the condition that each individual gives birth to at least one child. We also characterize the critical value for the existence of harmonic moments of the limit variable W under weaker conditions that in previous studies and generalize this result for processes starting with Z_0=k initial individuals. The third chapter is devoted to the study of the asymptotic of the harmonic moments of order r>0 of Z_n. We show the exact decay rate and give an expression of the limiting constants. The result reveals a phase transition phenomenon which is linked to the phase transitions in the lower large deviations established in earlier studies. As an application, we improve a lower large deviation result for the process (Z_n) under weaker hypothesis than those stated in the literature. Moreover, we also improve the rate of convergence in a central limit theorem for W-W_n and give the asymptotic of the large deviation for the ratio Zn+1/Z_n.

Consider an iterated function system (IFS) that does not necessarily contract uniformly, but instead contracts on average after a finite number of iterations. Under some technical assumptions, previous work by Barnsley, Demko, Elton and Geronimo has shown that such an IFS has a unique invariant probability measure, whilst many (such as Peigné, Hennion and Hervé, Guivarc'h and le Page, Santos and Walkden) have shown that (for different function spaces) the transfer operator associated with the IFS is quasi-compact. A result due to Keller and Liverani allows one to deduce whether the transfer operator remains quasi-compact under suitable, small perturbations. The first part of this thesis proves a large deviations result for IFSs that contract on average using skew product transfer operators, a technique used by Broise to prove a similar result for dynamical systems. The remaining chapters introduce a notion of 'coupled IFSs', an analogue of the traditional coupled map lattices where the base, unperturbed behaviour is determined by an underlying dynamical system. We use transfer operators and Keller and Liverani's theorem to prove that quasi-compactness of the transfer operator is preserved for 'product IFSs' under small perturbations and for coupled IFSs. This allows us to prove a central limit theorem with a rate of convergence for the coupled IFS.

Le but de cette thèse est de développer la théorie de Freidlin-Wentzell pour des modèles des épidémies, afin de prédire le temps mis par les perturbations aléatoires pour éteindre une situation endémique "stable". Tout d'abord nous proposons une nouvelle démonstration plus courte par rapport à celle établit récemment (sous une hypothèse un peu différente, mais satisfaite dans tous les exemples de modèles de maladie infectieuses que nous avons à l'esprit) par Kratz et Pardoux (2017) sur le principe de grandes déviations pour les modèles des épidémies. Ensuite nous établissons un principe de grandes déviations pour des EDS poissoniennes réfléchies au bord d'un ouvert suffisamment régulier. Nous établissons aussi un résultat concernant la zone du bord la plus probable par laquelle le processus solution de l'EDS de Poisson va sortir du domaine d'attraction d'un équilibre stable de sa loi des grands nombres limite. Nous terminons cette thèse par la présentation des méthodes "non standard aux différences finis", appropriés pour approcher numériquement les solutions de nos EDOs ainsi que par la résolution d'un problème de contrôle optimal qui permet d'avoir une bonne approximation du temps d'extinction d'un processus d'infection. / In this thesis, we develop the Freidlin-Wentzell theory for the "natural'' Poissonian random perturbations of the above ODE in Epidemic Dynamics (and similarly for models in Ecology or Population Dynamics), in order to predict the time taken by random perturbations to extinguish a "stable" endemic situation. We start by a shorter proof of a recent result of Kratz and Pardoux (under a somewhat different hypothesis which is satisfied in all the cases we have examined so far), which establishes the large deviations principle for epidemic models. Next, we establish the large deviations principle for reflected Poisonian SDE at the boundary of a sufficiently regular open set. Then, we establish the result for the most likely boundary area by which the process will exit the domain of attraction of a stable equilibrium of an ODE. We conclude this thesis with the presentation of the "non - standard finite difference" methods, suitable to approach numerically the solutions of our ODEs as well as the resolution of an optimal control problem which allows to have a good approximation of the time of extinction of an endemic situation.