Degenerate Irregular SDEs with Jumps and Application to Integro-Differential Equations of Fokker-Planck type

TL;DR

This paper studies stochastic differential equations with jumps and irregular coefficients, establishing existence and uniqueness of solutions and applying these results to Fokker-Planck type integro-differential equations.

Contribution

It introduces new existence and uniqueness results for irregular jump SDEs and their connection to Fokker-Planck equations.

Findings

Existence and uniqueness of generalized stochastic flows for irregular jump SDEs

Existence and uniqueness of $L^p$-solutions for Fokker-Planck type equations

Application to measure-valued solutions of integro-differential equations

Abstract

We investigate stochastic differential equations with jumps and irregular coefficients, and obtain the existence and uniqueness of generalized stochastic flows. Moreover, we also prove the existence and uniqueness of $L^p$-solutions or measure-valued solutions for second order integro-differential equation of Fokker-Planck type.