Persistence, permanence and extinction for differential or integrodifferential stochastic equations involving integrable Itô-Kurzweil-Henstock functions

• Grant number: 21/09422-1
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: December 01, 2021
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: Antonio Martins Alves Veloso dos Santos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 23/16185-1 - Relations between stochastic differential equations and generalized random differential equations with delays and impulses applied to biological mathematics, BE.EP.DD

Abstract

The main goals of this project are to obtain results on permanence, persistence and extinction of solutions of Stochastic Differential Equations (we write, for short, SDEs) or stochastic integrodifferential equations whose functions involved are integrable in the sense of Itô-Kurzweil-Henstock and to apply the results to population models. Recently, EDEs have been considered particular cases of a certain class of generalized ODEs, when these last were contextualized in the framework of the Itô-Kurzweil-Henstock integral. We intend to continue this study by investigating qualitative properties such as persistence, permanence, and extinction of solutions of EDEs or stochastic integrodifferential equations involving integrable functions in the Itô-Kurzweil-Henstock sense along with applications that will include in population models (AU)