Integration by parts formula with respect to jump times for stochastic differential equations

TL;DR

This paper develops an integration by parts formula based on jump times to analyze the regularity of solutions to stochastic differential equations with jumps.

Contribution

It introduces a novel integration by parts approach centered on jump times within an abstract framework for SDEs with jumps.

Findings

Provides a new method for studying regularity of jump SDE solutions

Establishes an integration by parts formula for jump processes

Facilitates analysis of the law of solutions to jump SDEs

Abstract

We establish an integration by parts formula based on jumps times in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps.