Martingales: Theorems and applications

• Grant number: 24/09519-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2024
• End date: August 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Elcio Lebensztayn
• Grantee: João Vitor Vieira de Castro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

In this project, we aim to study martingales, their fundamental results, and applications. We intend to examine different versions of the two main theorems in the field, the Optional Stopping Theorem and the Martingale Convergence Theorem. We will also delve into the concept of uniform integrability and maximal inequalities. Ultimately, our purpose in this proposal is to develop the theory from the perspective of modern probability, including the study of the general definition of conditional expectation and martingales with respect to sigma-algebras.