论文标题
抛物线寄生虫模型的空间平均值的高斯波动，具有neumann/dirichlet/周期性边界条件
Gaussian fluctuation for spatial average of parabolic Anderson model with Neumann/Dirichlet/periodic boundary conditions
论文作者
论文摘要
考虑抛物线Anderson模型$ \ partial_tu = \ frac {1} {2} \ partial_x^2u+u \ u \ u \，η$，newimann，dirichlet或周期性边界条件，由neumann，dirichlet或周期性边界条件，由时空时代白噪声$η$η$η$η$η$η$。使用malliavin-stein方法，我们建立了空间积分$ \ int_0^lu（t \ ,, x）\，\ mathrm {d} x $ as $ l $趋向于无限度的中心限制定理$ \ mathbb {r} $。
Consider the parabolic Anderson model $\partial_tu=\frac{1}{2}\partial_x^2u+u\, η$ on the interval $[0, L]$ with Neumann, Dirichlet or periodic boundary conditions, driven by space-time white noise $η$. Using Malliavin-Stein method, we establish the central limit theorem for the fluctuation of the spatial integral $\int_0^Lu(t\,, x)\, \mathrm{d} x$ as $L$ tends to infinity, where the limiting Gaussian distribution is independent of the choice of the boundary conditions and coincides with the Gaussian fluctuation for the spatial average of parabolic Anderson model on the whole space $\mathbb{R}$.
