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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)
Effective date (Start): December 01, 2021
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


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)

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