English

A Wong-Zakai Approximation of Stochastic Differential Equations Driven by a General Semimartingale

Probability 2019-02-19 v1

Abstract

We examine a Wong-Zakai type approximation of a family of stochastic differential equations driven by a general cadlag semimartingale. For such an approximation, compared with the pointwise convergence result by Kurtz, Pardoux and Protter [12, Theorem 6.5], we establish stronger convergence results under the Skorokhod M_1-topology, which, among other possible applications, implies the convergence of the first passage time of the solution to the stochastic differential equation.

Keywords

Cite

@article{arxiv.1902.06609,
  title  = {A Wong-Zakai Approximation of Stochastic Differential Equations Driven by a General Semimartingale},
  author = {Xianming Liu and Guangyue Han},
  journal= {arXiv preprint arXiv:1902.06609},
  year   = {2019}
}