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A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale

  • * Corresponding author: Xianming Liu

    * Corresponding author: Xianming Liu 
The first author is supported by NSF grants of China No. 11971186
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  • We examine a Wong-Zakai type approximation of a family of stochastic differential equations driven by a general càdlàg semimartingale. For such an approximation, compared with the pointwise convergence result by Kurtz, Pardoux and Protter [10,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 approximating stochastic differential equation.

    Mathematics Subject Classification: Primary: 60H10; Secondary: 34F05.


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