Stochastic stability via Lyapunov functions and applications

• Grant number: 21/11857-6
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2022
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Fabiano Borges da Silva
• Grantee: Elias Oliveira Vieira dos Santos
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

This is the training of a researcher at a level of excellence in the field of stochastic dynamic systems. The initial stage of the project consists of the study of stochastic differential equations, existence and uniqueness of solutions, Kolmogorov's reverse equation, Dynkin's formula and conditions of existence and uniqueness of a probabilistic solution for the classical Dirichlet problem. Subsequently, we will study, via the Lyapunov function, the qualitative properties of the solution of a SDE, such as stochastic stability (in the Has'minskii sense) and conditions for the existence of an invariant measure. And finally, we will apply these concepts and results to make a qualitative analysis of some solutions of SDE that model current problems in biology, engineering or economics, looking for new results. (AU)