Geodesic
First order convergence of weak Wong--Zakai approximations of L\'evy-driven Marcus SDEs
Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 32-60

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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 $f\in C_b^4$.
Keywords: Lévy process, Marcus (canonical) stochastic differential equation, Wong–Zakai approximation, first order convergence
Mots-clés : Euler scheme. 
@article{THSP_2019_24_2_a3,
     author = {Tetyana Kosenkova and Alexei Kulik and Ilya Pavlyukevich},
     title = {First order convergence of weak {Wong--Zakai} approximations of {L\'evy-driven} {Marcus} {SDEs}},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {32--60},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a3/}
}
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Tetyana Kosenkova; Alexei Kulik; Ilya Pavlyukevich. First order convergence of weak Wong--Zakai approximations of L\'evy-driven Marcus SDEs. Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 32-60. http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a3/