In this paper, we consider the strong convergence order of the exponential integrator for the stochastic heat equation driven by an additive fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. By showing the strong order one of accuracy of the exponential integrator under appropriote assumptions, we present the first super-convergence result in temporal direction on full discretizations for stochastic partial differential equations driven by infinite dimensional fractional Brownian motions with Hurst parameter $H\in(\frac12,1)$. The proof is a combination of Malliavin calculus, the $L^p(Ω)$-estimate of the Skorohod integral and the smoothing effect of the Laplacian operator.
High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise
Univ Lyon, Université Claude Bernard Lyon 1（里昂大学，克洛德·贝尔纳里昂大学）；CNRS UMR 5208, Institut Camille Jordan（法国国家科学研究中心联合研究实验室5208，卡米耶·若当研究所）；Université de Genève（日内瓦大学）
Strong convergence of an fractional exponential integrator scheme for the finite element discretization of time-fractional SPDE driven by standard and fractional Brownian motions
Weak convergence for a stochastic exponential integrator and finite element discretization of SPDE for multiplicative \& additive noise
Stellenbosh University（斯泰伦博斯大学）；Center for Research in Computational and Applied Mechanics (CERECAM)（计算与应用力学研究中心）；Department of Mathematics and Applied Mathematics, University of Cape Town（开普敦大学数学与应用数学系）；School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal（夸祖鲁-纳塔尔大学数学、统计与计算机科学学院）
Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise
Strong convergence rate of the Euler scheme for SDEs driven by additive rough fractional noises
研究了可加分数布朗运动驱动的偏微分方程Euler格式的强收敛速度，其中分数布朗运动具有Hurst参数$H\in(\frac13,\frac12)$，漂移系数不要求有界.利用Malliavin演算、粗糙路径理论和$2$ D Young积分，克服了分数阶布朗运动的低正则性和漂移系数的无界性所带来的困难.证明了Euler格式在漂移系数导数有界的情况下具有强$2H$阶，在线性情况下具有强$H+\frac12$阶.数值模拟支持的理论结果。
Strong convergence of some Magnus-type schemes for the finite element discretization of non-autonomous parabolic SPDEs driven by additive fractional Brownian motion and Poisson random measure
针对 fBm 与 Poisson 随机测度共同驱动的非自治半线性抛物型 SPDE，提出有限元结合随机 Magnus 型或半隐式 Euler 的全离散格式，并证明其强收敛阶。
Optimal strong convergence rates of some Euler-type timestepping schemes for the finite element discretization SPDEs driven by additive fractional Brownian motion and Poisson random measure
Strong convergence analysis of the stochastic exponential Rosenbrock scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise
