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arXiv · 1902.06609

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

Xianming Liu·Guangyue Han
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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.

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Xianming Liu, Guangyue Han. 2019-02-18. A Wong-Zakai Approximation of Stochastic Differential Equations Driven by a General Semimartingale. https://arxiv.org/abs/1902.06609

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