Relations between stochastic differential equations and generalized random differential equations with delays and impulses applied to biological mathematics

• Grant number: 23/16185-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: May 01, 2024
• End date: April 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: Antonio Martins Alves Veloso dos Santos
• Supervisor: Xiaoying Han
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Auburn University, United States
• Associated to the scholarship: 21/09422-1 - Persistence, permanence and extinction for differential or integrodifferential stochastic equations involving integrable Itô-Kurzweil-Henstock functions, BP.DD

Abstract

This project focuses on establishing and developing the foundational concepts of Itô-Henstock Random Ordinary Differential Equations (RODEs). The aim is to define a theoretical framework for RODEs, incorporating the Itô-Henstock integral into their integral forms. An additional objective is to explore the relationship between Itô-Henstock RODEs and Itô-Henstock Stochastic Differential Equations (SDEs). This exploration builds upon the established connection between RODEs and SDEs, with the goal of gaining insights into the interplay between these two types of equations within the Itô-Henstock framework.