| Volume 8, Number 1, 2018, Pages 202-228 DOI：10.11948/2018.202 |
| On a semilinear double fractional heat equation driven by fractional Brownian sheet |
| Dengfeng Xia,Litan Yan,Xiuwei Yin |
| Keywords:Mixed fractional heat equation, fractional Brownian sheet, H\"older regularity, Large deviation principle. |
| Abstract: |
| In this paper, we consider the stochastic heat equation of the form ∂u∂t=(Δα+Δβ)u+∂f∂x(t,x,u)+∂2W∂t∂x, where 1<β<α<2, W(t,x) is a fractional Brownian sheet, Δθ:=−(−Δ)θ/2 denotes the fractional Lapalacian operator and f:[0,T]×R×R→R is a nonlinear measurable function. We introduce the existence, uniqueness and H\"older regularity of the solution. As a related question, we consider also a large deviation principle associated with the above equation with a small perturbation via an equivalence relationship between Laplace principle and large deviation principle. |
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