Irregular Stochastic differential equations driven by a family of Markov processes

Abstract

Using heat kernel estimates, we prove the pathwise uniqueness for strong solutions of irregular stochastic differential equation driven by a family of Markov process, whose generator is a non-local and non-symmetric Lévy type operator. Due to the extra term $1_{[0,\sigma (X_{s-},z)]}(r)$ in multiplicative noise, we need to derive some new regularity results for the generator and use a trick of mixing $L_1$ and $L_2$-estimates by Kurtz and Protter \cite{Ku-Po}.

References in corpus (2)

• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient
• Integrability Conditions for SDEs and Semi-Linear SPDEs

Cited by in corpus (1)

• Spatial regularity of semigroups generated by Lévy type operators