Characterization of the support for Wick powers of the additive stochastic heat equation

2020/01/31 by Toyomu Matsuda, Matsuda, Toyomu
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2001.11705

openalex publication_date 2020/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Z be the stationary solution of the additive stochastic heat equation ∂_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^∞. 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 L²-phase.

Citations

• The support of singular stochastic PDEs
• Global well-posedness for the two-dimensional stochastic complex Ginzburg-Landau equation
• Global well-posedness of the two-dimensional stochastic complex Ginzburg-Landau equation with cubic nonlinearity

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