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- W2962741853 abstract "In this paper, we consider fractional parabolic equation of the form $ frac{partial u} {partial t}=-(-Delta )^{frac{alpha } {2}}u+udot W(t,x)$, where $-(-Delta )^{frac{alpha } {2}}$ with $alpha in (0,2]$ is a fractional Laplacian and $dot W$ is a Gaussian noise colored both in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result for space-time Hamiltonians driven by $alpha $-stable process. As a byproduct, we obtain the critical values for $theta $ and $eta $ such that $mathbb{E} exp left (theta left (int _0^1 int _0^1 |r-s|^{-beta _0}gamma (X_r-X_s)drdsright )^eta right )$ is finite, where $X$ is $d$-dimensional symmetric $alpha $-stable process and $gamma (x)$ is $|x|^{-beta }$ or $prod _{j=1}^d|x_j|^{-beta _j}$." @default.
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- W2962741853 date "2018-01-01" @default.
- W2962741853 modified "2023-09-26" @default.
- W2962741853 title "Temporal asymptotics for fractional parabolic Anderson model" @default.
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- W2962741853 doi "https://doi.org/10.1214/18-ejp139" @default.
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