Abstract
In this paper, we consider the stochastic heat equation of the form <i>∂u</i>/<i>∂t</i>=(∆<sub><i>α</i></sub> + ∆<sub><i>β</i></sub>)<i>u</i> + <i>∂f</i>/<i>∂x</i> (<i>t, x, u</i>) + <i>∂</i><sup>2</sup><i>W</i>/<i>∂t∂x</i>, where 1 < <i>β</i> < <i>α</i> < 2, <i>W</i>(<i>t, x</i>) is a fractional Brownian sheet, ∆<sub><i>θ</i></sub>:=-(-∆)<sup><i>θ</i>/2</sup> denotes the fractional Lapalacian operator and <i>f</i>:[0, <i>T</i>]×R×R → R is a nonlinear measurable function. We introduce the existence, uniqueness and Hölder 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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