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arXiv · 1610.07248

Irregular Stochastic differential equations driven by a family of Markov processes

Longjie Xie·Lihu Xu
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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 L\'evy 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}.

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Longjie Xie, Lihu Xu. 2016-10-23. Irregular Stochastic differential equations driven by a family of Markov processes. https://arxiv.org/abs/1610.07248

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