论文标题
表征对加性随机热方程的灯芯功率的支持
Characterization of the support for Wick powers of the additive stochastic heat equation
论文作者
论文摘要
令$ z $为添加剂随机加热方程的固定解决方案$ \ partial_t z =（δ-1）Z +ξ$在二维曲线上，其中$ξ$是时空白噪声。本文的目的是确定Wick Powers $ \ {z^{：k：} \} _ {k = 1}^{\ infty} $的支持。这导致了动态$ p（φ）_2 $方程的支持定理的基本证明。此外，我们表明该方法可用于确定$ l^2 $ - 相间的高斯乘法性混乱的法律的支持。
Let $Z$ be the stationary solution of the additive stochastic heat equation $\partial_t Z = (Δ- 1) Z + ξ$ on the two-dimensional torus, where $ξ$ is the space-time white noise. The aim of this paper is to determine the support of Wick powers $\{Z^{:k:}\}_{k=1}^{\infty}$. This leads to an elementary proof of a support theorem for the dynamic $P(Φ)_2$ equation. In addition, we show that the approach can be used to determine the support of the law of the Gaussian multiplicative chaos in the $L^2$-phase.
