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Article overview
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Space-time fractional diffusions in Gaussian noisy environment | | Le Chen
; Guannan Hu
; Yaozhong Hu
; Jingyu Huang
; | | Date: |
2 Aug 2015 | | Abstract: | This paper studies the linear stochastic partial differential equation of
fractional orders both in time and space variables $left(partial^eta +
frac{
u}{2} (-Delta)^{alpha/2}
ight) u(t,x)= lambda u(t,x)
dot{W}(t,x)$, where $dot W$ is a general Gaussian noise and $etain (1/2,
2)$, $alphain (0, 2]$. The existence and uniqueness of the solution, the
moment bounds of the solution are obtained by using the fundamental solutions
of the corresponding deterministic counterpart represented by the Fox
H-functions. Along the way, we obtain some new properties of the fundamental
solutions. | | Source: | arXiv, 1508.0252 | | Services: | Forum | Review | PDF | Favorites | |
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