论文标题
一些重新归一化的抛物线模型的力矩估计
Moment estimates for some renormalized parabolic Anderson models
论文作者
论文摘要
规则性结构理论可以在非常粗糙的环境中的以下抛物线安德森模型的定义：$ \ partial_ {t} u_ {t}（x）= \frac12Δu_{t}（x） + u_ {x） + u_ {t}（t}（x）（x）\，\ dot w_ dot w_ {t} { $ t \ in \ mathbb {r} _ {+} $和$ x \ in \ mathbb {r}^{d} $，其中$ \ dot w_ {t}（t}（x）$是高斯噪声，其时空时空函数很单独。在这种粗糙的背景下，当在Skorohod和Stratonovich Sense中解释随机热方程时，我们将提供一些有关$ u_ {t}（x）$的矩的信息。特别感兴趣的是一个关键案例，人们在很大程度上观察到了瞬间的爆炸。
The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: $\partial_{t} u_{t}(x) = \frac12 Δu_{t}(x) + u_{t}(x) \, \dot W_{t}(x)$, for $t\in\mathbb{R}_{+}$ and $x\in \mathbb{R}^{d}$, where $\dot W_{t}(x)$ is a Gaussian noise whose space time covariance function is singular. In this rough context, we shall give some information about the moments of $u_{t}(x)$ when the stochastic heat equation is interpreted in the Skorohod as well as the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.
