WEAK APPROXIMATIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL NOISE

作     者：Meng Cai Siqing Gan Xiaojie Wang Meng Cai;Siqing Gan;Xiaojie Wang

作者机构：School of Mathematics and StatisticsHNP-LAMACentral South UniversityChangshaChina 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2024年第42卷第3期

页      面：735-754页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by NSF of China(Grant Nos.11971488,12071488) by NSF of Hunan Province(Grant No.2020JJ2040) by the Fundamental Research Funds for the Central Universities of Central South University(Grant Nos.2017zzts318,2019zzts214) 

主　　题：Parabolic SPDEs Fractional Brownian motion Weak convergence rates Spec-tral Galerkin method Exponential Euler method Malliavin calculus 

摘      要：This paper aims to analyze the weak approximation error of a fully discrete scheme for a class of semi-linear parabolic stochastic partial differential equations(SPDEs)driven by additive fractional Brownian motions with the Hurst parameter H∈(1/2,1).The spatial approximation is performed by a spectral Galerkin method and the temporal discretization by an exponential Euler *** far as we know,the weak error analysis for approximations of fractional noise driven SPDEs is absent in the literature.A key difficulty in the analysis is caused by the lack of the associated Kolmogorov *** the present work,a novel and efficient approach is presented to carry out the weak error analysis for the approximations,which does not rely on the associated Kolmogorov equations but relies on the Malliavin *** the best of our knowledge,the rates of weak convergence,shown to be higher than the strong convergence rates,are revealed in the fractional noise driven SPDE setting for the first *** examples corroborate the claimed weak orders of convergence.