Seminar: Numerical approximation for stochastic differential equations with irregular coefficients

Thời gian: 14:00 đến 16:00 Ngày 07/08/2024

Địa điểm: Room C102, VIASM

Báo cáo viên: Prof. Dai Taguchi, Kansai University, Japan

Title: A generalized coupling approach for the weak approximation of stochastic functional differential equations

Abstract: In this talk, we consider a numerical approximation for stochastic functional differential equations (SFDEs). Under the assumption that the coefficients are (locally) H\"older continuous and the diffusion coefficient satisfies (non-uniform) ellipticity condition, we provide an estimate for the L\'evy--Prokhorov metric between the weak solution of SFDE and the corresponding Euler--Maruyama scheme. The idea of the proof is based on the ``generalized coupling approach" which has been studied by Butkovsky--Kulik--Scheutzow (2020). We apply our results to Markovian SDEs (e.g. Dyson's Brownian motion), non-Markovian SDEs (stochastic delay/integro differential equations), reflected SDEs and perturbed diffusion processes. This talk is based on joint work with Yushi Hamaguchi (Kyoto University).