论文标题
抛物线型安德森模型的空间平均值的功能性中心限制定理，Delta初始条件$ d \ geq 1 $
Functional central limit theorems for spatial averages of the parabolic Anderson model with delta initial condition in dimension $d\geq 1$
论文作者
论文摘要
令$ \ { $ f $。令$ s_ {n，t}：= n^{ - d} \ int _ {{[[0，n]}^d} {[u（t，x）-1]} {\ rm d} x $表示$ {{\ Mathb r}^d} d} $ on $ {{\ rm d} $表示空间平均值。我们根据$ f $和空间尺寸$ d $的定量分析获得了各种空间平均值的功能中心限制定理（CLT）。特别是，当$ f $由riesz kernel给出时，即$ f（{\ rm x}）= {\ vert x \ vert}^{ - β} { - β} {\ rm d} x $，$β\ in（in（0,2 \ wedge d）$，该功能clt也基于索引。
Let $\{u(t,x)\}_{t>0,x\in{{\mathbb R}^{d}}}$ denote the solution to a $d$-dimensional parabolic Anderson model with delta initial condition and driven by a multiplicative noise that is white in time and has a spatially homogeneous covariance given by a nonnegative-definite measure $f$. Let $S_{N,t}:=N^{-d}\int_{{[0,N]}^d}{[U(t,x)-1]}{\rm d}x$ denote the spatial average on ${{\mathbb R}^{d}}$. We obtain various functional central limit theorems (CLTs) for spatial averages based on the quantitative analysis of $f$ and spatial dimension $d$. In particular, when $f$ is given by Riesz kernel, that is, $f({\rm x})={\Vert x \Vert}^{-β}{\rm d}x$, $β\in(0,2\wedge d)$, the functional CLT is also based on the index $β$.
