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

Tetyana Kosenkova, Alexei Kulik, Ilya Pavlyukevich
Theory of Stochastic Processes
Vol.24 (40), no.2, 2019, pp.32-60
For solutions X=(X_t)_{t ∈ [0,T]} of a Lévy-driven Marcus (canonical) stochastic differential equation we study the Wong-Zakai type time discrete approximations X = (X_kh)_{0 ≤ k ≤ T/h}, h>0, and establish the first order convergence |E_x f(X_T)- E_xf(X^h_T)| ≤ C h for f ∈ C_b⁴.