Weak Convergence for a Class of Stochastic Fractional Equations Driven by Fractional Noise
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 t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/479873 |
| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |