https://repositorio.ufba.br/handle/ri/5201 2026-05-03T15:58:03Z 2026-05-03T15:58:03Z Santos, Agábio Brasil dos https://repositorio.ufba.br/handle/ri/44401 2026-04-20T22:28:48Z 2025-11-11T00:00:00Z

Título: A teoria do transporte ótimo aplicada ao estudo de sistemas de funções iteradas Autor(es): Santos, Agábio Brasil dos Primeiro Orientador: Silva, Edgar Matias da Abstract: This work consists of a study of Iterated Function Systems that contract on average, using concepts and results from Optimal Transport Theory for this analysis. To support the discussion, it was necessary to revisit notions such as complete metric spaces, weak topology, as well as concepts from Measure Theory, Ergodic Theory, and Probability Theory. Within the latter, the notions of homogeneous Markov chains and the stationary measures associated with these chains are explored. Based on these preliminary concepts, optimal coupling is defined, demonstrating that, under certain conditions, the existence of such coupling is always guaranteed. The Wasserstein distance is also introduced, which plays an essential role in the subsequent results. Equipped with the tools of Optimal Transport Theory, this work investigates the stationary measures of Iterated Function Systems that contract on average, proving that, in this context, there is existence and uniqueness of a stationary measure, in addition to obtaining estimates for its moments of order q. Finally, the developed concepts are applied to the study of skew-products that have contractive fibers, showing that such systems admit a single "stationary measure'' with limited support. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação

2025-11-11T00:00:00Z Antunes, Gleberson Gregorio da Silva https://repositorio.ufba.br/handle/ri/44277 2026-03-23T20:36:43Z 2026-02-24T00:00:00Z

Título: Operadores Dunford-Pettis em reticulados de Banach Autor(es): Antunes, Gleberson Gregorio da Silva Primeiro Orientador: Ribeiro, Joilson Oliveira Abstract: A Dunford–Pettis operator is a linear operator that maps weakly convergent sequences into norm-convergent sequences. This work investigates the properties of positive operators defined on Banach lattices, with an emphasis on domination results. Specifically, we analyze the behavior of operators S and T satisfying 0 ≤ S ≤ T, seeking to determine how the properties of the dominating operator T, such as compactness or being a Dunford–Pettis operator, influence the operator S and its powers. Editora / Evento / Instituição: UNIVERSIDADE FEDERAL DA BAHIA Tipo: Dissertação

2026-02-24T00:00:00Z Azevedo, Arthur Rios de https://repositorio.ufba.br/handle/ri/44276 2026-03-23T20:04:56Z 2025-12-18T00:00:00Z

Título: Testes não paramétricos em análise de sobrevivência no contexto de inferência causal Autor(es): Azevedo, Arthur Rios de Primeiro Orientador: Amorim, Leila Denise Alves Ferreira Abstract: Research aimed at estimating causal effects of interventions on time-to-event outcomes in observational studies faces challenges, notably when the goal is to compare groups in the presence of confounding. Propensity score–based methodologies are well established in the literature and provide a robust framework for causal inference in observational studies. Weighting procedures have already been employed in nonparametric methods, such as the Kaplan-Meier estimator, allowing the construction of pseudo-populations using propensity scores, which yield adjusted, unbiased estimates in the presence of confounding. However, their integration with nonparametric hypothesis tests in survival analysis is still limited to the Log-Rank test and remains an area in need of methodological developments. In this dissertation, a generalization of nonparametric tests adjusted by the inverse probability of treatment weighting is developed, with a focus on comparing survival functions under different hazard patterns. The proposed methodology is assessed through simulation studies that consider alternative hypotheses involving proportional hazards, early and late separation, and crossing survival curves, as well as different censoring and sample size scenarios. The results show substantial gains in test power when the separation pattern is aligned with the weighting scheme used, suggesting that tests adjusted with appropriate weights can outperform classical approaches in the detection of causal effects. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação

2025-12-18T00:00:00Z Reis, Gábrio Ravel Souza https://repositorio.ufba.br/handle/ri/44058 2026-02-20T11:30:13Z 2025-08-25T00:00:00Z

Título: A influência da geometria fractal na recorrência de Poincaré. Autor(es): Reis, Gábrio Ravel Souza Primeiro Orientador: Silva, Edgar Matias da Abstract: This work investigates how the fractal geometry of a space influences the speed at which orbits return to small neighborhoods of their initial points. The object of study is a dynamical system that preserves a probability measure. The classical Poincaré Recurrence Theorem is a qualitative result, guaranteeing only that, for almost every point in the system, the return time is finite. Here, we move toward a quantitative description: we show that, along a subsequence, the distance between a typical orbit at time n and its initial point decays in a polynomial or subpolynomial manner, with the decay rate estimated by the Hausdorff dimension of the space. More precise estimates can be obtained by considering the Hausdorff dimension of the invariant measure. In addition, we use the theory developed for the deterministic case to study the random setting, in which orbits are generated by independent and identically distributed choices of functions. We show that the recurrence of random orbits exhibits the same behavior observed in the deterministic case. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação

2025-08-25T00:00:00Z