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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Processos aleat?rios n?o-markovianos: perfis de mem?ria

Lima, Gislene Micarla Borges de 14 January 2013 (has links)
Made available in DSpace on 2015-03-03T15:16:26Z (GMT). No. of bitstreams: 1 GisleneMBL_TESE.pdf: 4796926 bytes, checksum: 3d989d7de8f6bc7076e45b9a8f985c7f (MD5) Previous issue date: 2013-01-14 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / One of the mechanisms responsible for the anomalous diffusion is the existence of long-range temporal correlations, for example, Fractional Brownian Motion and walk models according to Elephant memory and Alzheimer profiles, whereas in the latter two cases the walker can always "remember" of his first steps. The question to be elucidated, and the was the main motivation of our work, is if memory of the historic initial is condition for observation anomalous diffusion (in this case, superdiffusion). We give a conclusive answer, by studying a non-Markovian model in which the walkers memory of the past, at time t, is given by a Gaussian centered at time t=2 and standard deviation t which grows linearly as the walker ages. For large widths of we find that the model behaves similarly to the Elephant model; In the opposite limit (! 0), although the walker forget the early days, we observed similar results to the Alzheimer walk model, in particular the presence of amnestically induced persistence, characterized by certain log-periodic oscillations. We conclude that the memory of earlier times is not a necessary condition for the generating of superdiffusion nor the amnestically induced persistence and can appear even in profiles of memory that forgets the initial steps, like the Gausssian memory profile investigated here. / Um dos mecanismos respons?veis pela difus?o an?mala ? a exist?ncia de correla??es temporais de longo alcance como, por exemplo, no movimento browniano fracion?rio e nos modelos de caminhadas aleat?rias segundo os perfis de mem?ria do elefante e de alzehimer, sendo que nestes dois ?ltimos casos o caminhante guarda a mem?ria dos seus primeiros passos. Uma quest?o a ser elucidada, e que foi a principal motiva??o de nosso trabalho, ? se a lembran?a do hist?rico inicial constitui-se em condi??o necess?ria para a observa??o de difus?o an?mala (no caso, superdifus?o). N?s damos uma resposta conclusiva, ao estudarmos um modelo de caminhada n?omarkoviana em que a mem?ria do passado do caminhante, no instante t, ? dada por uma gaussiana centrada no tempo t=2 e com desvio padr?o t que cresce linearmente com a idade do caminhante. Para grandes valores de vemos que este modelo se comporta de forma similar ao modelo de elefante; No limite oposto ( ! 0), embora o caminhante esque?a os tempos iniciais, observamos resultados semelhantes ao modelo de caminhada de alzheimer, em particular a presen?a de persist?ncia induzida por amn?sia, caracterizada por certas oscila??es log-peri?dicas. Conclu?mos assim que a mem?ria de tempos iniciais n?o ? uma condi??o necess?ria para o surgimento da superdifus?o nem da persist?ncia induzida por amn?sia, podendo aparecer mesmo em perfis de mem?ria que esquecem os passos iniciais, como o perfil gausssiano aqui investigado.
2

Caminhantes aleat?rios com perfil de mem?ria binomial

Gomes, Rebecca de Moura Diniz 27 May 2016 (has links)
Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-12-15T18:17:07Z No. of bitstreams: 1 RebeccaDeMouraDinizGomes_DISSERT.pdf: 2411622 bytes, checksum: 6b5e6ef2c6fd430fe0ff200b6352cd44 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-12-20T21:33:44Z (GMT) No. of bitstreams: 1 RebeccaDeMouraDinizGomes_DISSERT.pdf: 2411622 bytes, checksum: 6b5e6ef2c6fd430fe0ff200b6352cd44 (MD5) / Made available in DSpace on 2016-12-20T21:33:44Z (GMT). No. of bitstreams: 1 RebeccaDeMouraDinizGomes_DISSERT.pdf: 2411622 bytes, checksum: 6b5e6ef2c6fd430fe0ff200b6352cd44 (MD5) Previous issue date: 2016-05-27 / Grande tem sido o interesse nas difus?es an?malas, pois se apresentam nas mais diversas ?reas do conhecimento. A introdu??o de perfil de mem?ria no caminhante aleat?rio torna-o numa din?mica estoc?stica n?o-markoviana, cujas correla??es criam superdifus?o, persistencia e log-periodicidade. Apresentamos uma revis?o da literatura sobre os perfis de mem?ria e introduzimos nosso modelo. O modelo de mem?ria binomial pode selecionar diferentes regi?es de perda de mem?ria, desde a inicial at? a recente. Dessa forma, investigamos o impacto da posi??o da perda de mem?ria no comportamento superdifusivo do caminhante aleat?rio e unificamos muitos dos resultados da literatura. Obtivemos que mem?rias iniciais geram maior superdifus?o medidas pelo coeficiente de Hurst, enquanto que mem?rias recentes tendem a diminuir a superdifus?o, tornando mais caminhantes adeptos da difus?o normal. Tamb?m investigamos o regime de mem?ria curta inicial, com largura tendendo a zero. Observamos log-periodicidade para alguns caminhantes sugerindo regimes diferentes de comportamento log-periodico, incluindo aqueles considerados de difus?o normal. Uma particularidade do modelo binomial s?o os resutados extremamente sim?tricos para o diagrama Hxr. / Great has been the interest in anomalous diffusion because they are present in several areas of knowledge. The introduction of a memory profile in random walk environment give them a non-Markovian stochastic dynamics, whose temporal correlations may create superdiffusion, persistence and log-periodicity. We present an overview of memory profile literature and introduce our model. The binomial memory model can select different memory loss regions, from the old to the recent one. Thus, we investigate the impact of memory loss location on superdiffusive behavior of a random walker and unify some literature results. We verify that old memory generates higher superdiffusion measured by the Hurst coefficient, while recent memory tends to decrease superdiffusion, causing more walkers to undergo normal diffusion. We also investigate the short initial memory region, with zero tending standard deviation. We observe log-periodicity for some walkers suggesting different regions of log-periodic behavior, including those considered as normal diffusion. A particularity of the binomial model is an extremely symmetric result to Hxr diagram.

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