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

For solutions $X=(X_t)_{t\in[0,T]}$ of a Lévy-driven Marcus (canonical) stochastic differential equation 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 $|\mathbf{E}_x f(X_T)-\mathbf{E}_x f(X^h_T)|\leq C h$ for $f\in C_b^4$.