2024/02/19 by Thanh Dang, Lingjiong Zhu, Dang, Thanh +1
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2402.12502
openalex publication_date 2024/02/19 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28
Via a Bismut-Elworthy-Li formula from [KPP23], we derive uniform gradient estimates for transition semigroups associated with stochastic differential equations driven by a large class of cylindrical Lévy processes which includes the important case of cylindrical α-stable processes. As the first application, we formulate a Stein's method for quantitative approximation of the invariant measure of these stochastic differential equations in Wasserstein distance. As the second and main application, we study Euler-Maruyama numerical schemes of stochastic differential equations driven by stable Lévy processes with i.i.d. stable components and obtain a uniform-in-time approximation error in Wasserstein distance. Our approximation error has a linear dependence on the stepsize, which is expected to be tight, as can be seen from an explicit calculation for the case of an Ornstein-Uhlenbeck process.