Kavli Affiliate: Ran Wang
| First 5 Authors: Ran Wang, , , ,
| Summary:
Consider the stochastic partial differential equation
begin{equation*}
frac{partial }{partial t}u_t(x)= -(-Delta)^{frac{alpha}{2}}u_t(x)
+bleft(u_t(x)right)+sigmaleft(u_t(x)right) dot F(t, x), tge0,
xin mathbb R^d,
end{equation*}
where $-(-Delta)^{frac{alpha}{2}}$ denotes the fractional Laplacian with
the power $alpha/2in (1/2,1]$, and the driving noise $dot F$ is a centered
Gaussian field which is white in time and with a spatial homogeneous covariance
given by the Riesz kernel. We study the detailed behavior of the approximation
spatial gradient $u_t(x)-u_t(x-e mathbf e)$ at any fixed time $t>0$, as
$edownarrow 0$, where $mathbf e$ is the unit vector in $mathbb R^d$. As
applications, we deduce the law of iterated logarithm and the behavior of the
$q$-variations of the solution in space.
| Search Query: ArXiv Query: search_query=au:”Ran Wang”&id_list=&start=0&max_results=10