A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$

DOI10.1137/21M1422616WikidataQ114074026 ScholiaQ114074026MaRDI QIDQ5088625

Weihua Deng, Daxin Nie

Publication date: 13 July 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.13676

zbMATH Keywords

fractional Gaussian noisesharp error estimatestochastic nonlinear fractional diffusion equationunified regularity analysis

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fractional partial differential equations (35R11) Numerical analysis (65-XX)

Related Items (5)

Nontrivial Equilibrium Solutions and General Stability for Stochastic Evolution Equations with Pantograph Delay and Tempered Fractional Noise ⋮ Asymptotic behaviour of time fractional stochastic delay evolution equations with tempered fractional noise ⋮ An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion ⋮ An efficient numerical algorithm for the model describing the competition between super- and sub-diffusions driven by fractional Brownian sheet noise ⋮ \(H^1\)-analysis of H3N3-\(2_\sigma\)-based difference method for fractional hyperbolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• Space-time fractional stochastic partial differential equations
• On the Schrödinger equation and the eigenvalue problem
• Incomplete iterative solution of subdiffusion
• Convolution quadrature and discretized operational calculus. I
• Convolution quadrature and discretized operational calculus. II
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
• Potential theory of subordinate killed Brownian motion in a domain
• Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion
• Measuring anti-correlations in the nordic electricity spot market by wavelets
• An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise
• Spectral collocation method for stochastic partial differential equations with fractional Brownian motion
• Fractional time stochastic partial differential equations
• Finite element approximations for fractional evolution problems
• Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations
• Stochastic calculus for fractional Brownian motion and related processes.
• Multiple fractional integral with Hurst parameter less than \(\frac {1}{2}\)
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• Finite element approximations for second-order stochastic differential equation driven by fractional Brownian motion
• Galerkin Finite Element Approximations for Stochastic Space-Time Fractional Wave Equations
• Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise
• Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
• Approximating Stochastic Evolution Equations with Additive White and Rough Noises
• Variational formulation for the stationary fractional advection dispersion equation
• Fractional Brownian Motions, Fractional Noises and Applications

This page was built for publication: A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$