论文标题
Delta初始条件的抛物线型安德森模型的空间层状和中央限制定理
Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition
论文作者
论文摘要
令$ \ { （2πt）^{ - 1/2} \ exp \ { - x^2/（2t）\} $表示线上的标准高斯热核。我们在同伴论文\ cite {cknp，cknp_b}中使用这些方法的非平地改编，以证明每个$ t> 0 $的随机字段$ x \ mapsto u（t \ ,, x）/p_t（x）/p_t（x）$是每个$ t> 0 $。我们根据在黄，Nualart和Viitasaari \ cite {HNV2018}中引入的Malliavin-Stein方法建立了相关的定量中心限制定理。
Let $\{u(t\,, x)\}_{t >0, x \in\mathbb{R}}$ denote the solution to the parabolic Anderson model with initial condition $δ_0$ and driven by space-time white noise on $\mathbb{R}_+\times\mathbb{R}$, and let $p_t(x):= (2πt)^{-1/2}\exp\{-x^2/(2t)\}$ denote the standard Gaussian heat kernel on the line. We use a non-trivial adaptation of the methods in our companion papers \cite{CKNP,CKNP_b} in order to prove that the random field $x\mapsto u(t\,,x)/p_t(x)$ is ergodic for every $t >0$. And we establish an associated quantitative central limit theorem following the approach based on the Malliavin-Stein method introduced in Huang, Nualart, and Viitasaari \cite{HNV2018}.
