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=(Xt)t ∈ [0,T] of a Lévy-driven Marcus (canonical) stochastic differential equation we study the Wong-Zakai type time discrete approximations X = (Xkh)0 ≤ k ≤ T/h, h>0, and establish the first order convergence |Ex f(XT)- Exf(XhT)| ≤ C h for f ∈ Cb4.