Topics in stochastic processes

• Grant number: 20/12010-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): December 01, 2020
• Effective date (End): November 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Elcio Lebensztayn
• Grantee: Vicenzo Bonasorte Reis Pereira
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 17/10555-0 - Stochastic modeling of interacting systems, AP.TEM

Abstract

We aim to study stochastic processes, with emphasis on the theory of random walks on the line, and on the Bienaymé-Galton-Watson branching processes. For the random walks, we intend to work with combinatorial properties, the Reflection Principle, generating functions, return and hitting times, recurrence and transience. For the branching processes, we are interested in studying the basic definitions, results about the moments, the extinction and survival of the process, and examples. We also plan to study the problem of the existence of phase transition and to analyze different applications of stochastic systems.