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

2020/02/07 by Tetyana Kosenkova, Kosenkova, Tetyana, Alexei Kulik +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2002.02652

Abstract

For solutions X=(X_t)_t∈[0,T] of Lévy-driven Marcus stochastic differential equations 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 f(X_T)-E f(X^h_T)|≤ C h for f∈ C_b⁴.

Cited by

• Rates of convergence for multivariate SDEs driven by Lévy processes in the small-time stable domain of attraction

Related

• Strong uniform Wong--Zakai approximations of Lévy-driven Marcus SDEs
• Wong-Zakai approximations with convergence rate for stochastic partial differential equations
• A Wong-Zakai Approximation of Stochastic Differential Equations Driven by a General Semimartingale
• Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II
• Wong-Zakai type convergence in infinite dimensions