First order convergence of weak Wong--Zakai approximations of L\'evy driven Marcus SDEs

Tetyana Kosenkova; Alexei Kulik; Ilya Pavlyukevich

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arXiv · 2002.02652

First order convergence of weak Wong--Zakai approximations of L\'evy driven Marcus SDEs

Tetyana Kosenkova·Alexei Kulik·Ilya Pavlyukevich

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Abstract

For solutions $X=(X_t)_{t\in[0,T]}$ of L\'evy-driven Marcus stochastic differential equations we study the Wong--Zakai type time discrete approximations $\bar X=(\bar X_{kh})_{0\leq k\leq T/h}$, $h>0$, and establish the first order convergence $|E f(X_T)-E f(X^h_T)|\leq C h$ for $f\in C_b^4$.

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Tetyana Kosenkova, Alexei Kulik, Ilya Pavlyukevich. 2020-02-07. First order convergence of weak Wong--Zakai approximations of L\'evy driven Marcus SDEs. https://arxiv.org/abs/2002.02652

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