
Numerical analysis for stochastic timespace fractional diffusion equation driven by fractional Gaussion noise
In this paper, we consider the strong convergence of the timespace frac...
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A unified convergence analysis for the fractional diffusion equation driven by fractional Gaussion noise with Hurst index H∈(0,1)
Here, we provide a unified framework for numerical analysis of stochasti...
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Numerical approximation for fractional diffusion equation forced by a tempered fractional Gaussian noise
This paper discusses the fractional diffusion equation forced by a tempe...
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Strong convergence of some Eulertype schemes for the finite element discretization of timefractional SPDE driven by standard and fractional Brownian motion
In this work, we provide the first strong convergence result of numerica...
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Higher order approximation for stochastic wave equation
The infinitesimal generator (fractional Laplacian) of a process obtained...
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Optimal strong convergence rates of some Eulertype timestepping schemes for the finite element discretization SPDEs driven by additive fractional Brownian motion and Poisson r
In this paper, we study the numerical approximation of a general second ...
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A Numerical Method for a Nonlocal Diffusion Equation with Additive Noise
We consider a nonlocal evolution equation representing the continuum lim...
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Strong convergence order for the scheme of fractional diffusion equation driven by fractional Gaussion noise
Fractional Gaussian noise models the time series with longrange dependence; when the Hurst index H>1/2, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving stochastic fractional diffusion equation driven by fractional Gaussian noise. Using the operator theoretical approach, we present the regularity estimate of the mild solution and the fully discrete scheme with finite element approximation in space and backward Euler convolution quadrature in time. The 𝒪(τ^Hρα) convergence rate in time and 𝒪(h^min(2,22ρ,H/α)) in space are obtained, showing the relationship between the regularity of noise and convergence rates, where ρ is a parameter to measure the regularity of noise and α∈(0,1). Finally, numerical experiments are performed to support the theoretical results.
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