论文标题
具有半拉普拉斯和周期性噪音的连续抛物线安德森模型
The continuum parabolic Anderson model with a half-Laplacian and periodic noise
论文作者
论文摘要
我们构建了重新归一化的连续分数抛物线模型的解决方案，该模型由$ \ partial_t u = - （ - δ）^{1/2} u+ξu$正式给出，其中$ξ$是一种周期性的空间白噪声。确切地说，我们将极限构建为$ \ varepsilon \ to 0 $ to $ \ partial_t u_ \ varepsilon = - （ - δ）^{1/2}^{1/2} u_ \ varepsilon+（ξ_\之一） $ \ varepsilon $和$ c_ \ varepsilon $的$之一的$ξ$是对数分化的重新归一化常数。我们使用基于Hairer和Labbé的简单重归其化方案，“在$ \ Mathbf {r}^{2} $上的Continuum parrabolic Anderson模型的简单结构。”
We construct solutions of a renormalized continuum fractional parabolic Anderson model, formally given by $\partial_t u=-(-Δ)^{1/2}u+ξu$, where $ξ$ is a periodic spatial white noise. To be precise, we construct limits as $\varepsilon\to 0$ to solutions of $\partial_t u_\varepsilon=-(-Δ)^{1/2}u_\varepsilon+(ξ_\varepsilon-C_\varepsilon)u_\varepsilon$, where $ξ_\varepsilon$ is a mollification of $ξ$ at scale $\varepsilon$ and $C_\varepsilon$ is a logarithmically diverging renormalization constant. We use a simple renormalization scheme based on that of Hairer and Labbé, "A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^{2}$."
