Kavli Affiliate: Ran Wang
| First 5 Authors: Chang Liu, Chang Liu, , ,
| Summary:
We study the linear stochastic fractional heat equation $$
fracpartialpartial
tu(t,x)=-(-Delta)^fracalpha2u(t,x)+dotW(t,x), quad t>0, quad
xinmathbbR, $$ where $-(-Delta)^fracalpha2$ denotes the fractional
Laplacian with power $alphain (1,2)$, and the driving noise $dotW$ is a
centered Gaussian field that is white in time and has the covariance of a
fractional Brownian motion with Hurst parameter
$Hinleft(frac2-alpha2,frac12right)$. We establish exact
asymptotics for the solution as $t, x to infty$ and derive sharp growth rates
for the H"older coefficients. The proofs are based on Talagrand’s majorizing
measure theorem and Sudakov’s minoration theorem.
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