Decomposition of flows in averaging principles and stochastic transport equation

• Grant number: 22/13413-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2022
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Josué Knorst
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 20/04426-6 - Stochastic dynamics: analytical and geometrical aspects with applications, AP.TEM
• Associated scholarship(s): 23/14629-0 - Mean-field limit of particle systems, McKean-Vlasov SDE, and Mean-field Games under common noise, BE.EP.PD

Abstract

We will study the decomposition of stochastic flows into a differentiable manifold and use the decomposition to obtain a kind of averaging principle. We will also study the existence and uniqueness of the nonlinear stochastic transport equation.