weak convergence for a class of stochastic fractional equations driven by fractional noise
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2014
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Abstract
We consider a class of stochastic fractional equations driven by fractional noise on t,x∈0,T×0,1 ∂u/∂t=Dδαu+ft,x,u+∂2BHt,x/∂t ∂x, with Dirichlet boundary conditions. We formally replace the random perturbation by a family of sequences based on Kac-Stroock processes in the plane, which approximate the fractional noise in some sense. Under some conditions, we show that the real-valued mild solution of the stochastic fractional heat equation perturbed by this family of noises converges in law, in the space 𝒞0,T×0,1 of continuous functions, to the solution of the stochastic fractional heat equation driven by fractional noise.
| Reference Key |
sun2014advancesweak
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|---|---|
| Authors | ;Xichao Sun;Junfeng Liu |
| Journal | theater |
| Year | 2014 |
| DOI |
10.1155/2014/479873
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| URL | |
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