First order convergence of weak Wong--Zakai approximations of Lévy driven Marcus SDEs

Abstract

For solutions $X=(X_t{)}_{t\in [0,T]}$ of Lévy-driven Marcus stochastic differential equations we study the Wong--Zakai type time discrete approximations $\bar{X}=({\bar{X}}_{kh}{)}_{0\le k\le T/h}$, $h>0$, and establish the first order convergence $|Ef(X_T)-Ef(X_T^h)|\le Ch$ for $f\in C_b^4$.