Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations

DOI10.1007/s10543-016-0639-4zbMath1367.60092arXiv1605.04388OpenAlexW2399330746MaRDI QIDQ2359763

Fengze Jiang, Rui-sheng Qi, Xiao-Jie Wang

Publication date: 22 June 2017

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04388

zbMATH Keywords

regularityfractional Brownian motionstrong approximationoptimal convergence ratesparabolic stochastic PDEs

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (10)

The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise ⋮ Regularity analysis for SVEEs with additive fBms and strong error estimates for the numerical approximations ⋮ A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$ ⋮ An efficient numerical algorithm for the model describing the competition between super- and sub-diffusions driven by fractional Brownian sheet noise ⋮ On spectral Petrov-Galerkin method for solving optimal control problem governed by fractional diffusion equations with fractional noise ⋮ Optimal strong convergence rates of numerical methods for semilinear parabolic SPDE driven by Gaussian noise and Poisson random measure ⋮ Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion ⋮ 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 ⋮ A full discretization of the rough fractional linear heat equation ⋮ Optimal strong convergence of finite element methods for one-dimensional stochastic elliptic equations with fractional noise

Cites Work

• Strong and weak approximation of semilinear stochastic evolution equations
• Mild solutions for a class of fractional SPDEs and their sample paths
• Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
• The numerical approximation of stochastic partial differential equations
• Stochastic heat equation driven by fractional noise and local time
• Semigroups of linear operators and applications to partial differential equations
• A parabolic stochastic differential equation with fractional Brownian motion input
• Evolution equations driven by a fractional Brownian motion
• Optimal approximation of SDE's with additive fractional noise
• The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation
• An Introduction to Computational Stochastic PDEs
• FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES
• Semilinear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion
• Approximating Stochastic Evolution Equations with Additive White and Rough Noises
• Stochastic Equations in Infinite Dimensions
• Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
• Stochastic Calculus for Fractional Brownian Motion and Applications
• Galerkin Finite Element Methods for Parabolic Problems
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations