
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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Numerical analysis of a wave equation for lossy media obeying a frequency power law
We study a wave equation with a nonlocal time fractional damping term th...
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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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Highfrequency analysis of parabolic stochastic PDEs with multiplicative noise: Part I
We consider the stochastic heat equation driven by a multiplicative Gaus...
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Generalized kvariations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus
We analyze the generalized kvariations for the solution to the wave equ...
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Ergodicity of stochastic CahnHilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises
We study the asymptotic properties of the stochastic CahnHilliard equat...
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Generalized Stochastic Processes as Linear Transformations of White Noise
We show that any (real) generalized stochastic process over ℝ^d can be e...
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Galerkin finite element approximation for semilinear stochastic timetempered fractional wave equations with multiplicative white noise and fractional Gaussian noise
To model wave propagation in inhomogeneous media with frequencydependent powerlaw attenuation, it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time. The model studied in this paper is semilinear stochastic spacetime fractional wave equations driven by infinite dimensional multiplicative white noise and fractional Gaussian noise, because of the potential fluctuations of the external sources. The purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave equation. We first provide a complete solution theory, e.g., existence, uniqueness, and regularity. Then the spacetime multiplicative white noise and fractional Gaussian noise are discretized, which results in a regularized stochastic fractional wave equation while introducing a modeling error in the meansquare sense. We further present a complete regularity theory for the regularized equation. A standard finite element approximation is used for the spatial operator, and the meansquare priori estimates for the modeling error and for the approximation error to the solution of the regularized problem are established.
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