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

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 $\bar{X}=({\bar{X}}_{kh}{)}_{0\le k\le T\mathrm{/}h}$, $h>0$, and establish the first order convergence $\mathrm{\mid }Ef(X_T)-Ef(X_T^h)\mathrm{\mid }\le Ch$ for $f\in C_b^4$.