论文标题
GPAM精确拉普拉斯的恒定系数
The constant coefficient in precise Laplace asymptotics for gPAM
论文作者
论文摘要
本文恢复了彼得·弗里斯（Peter Friz）和作者发起的广义抛物线安德森模型（GPAM）的精确拉普拉斯渐近学分析。更确切地说，我们在某些显式操作员的痕迹和Carleman-Fredholm的决定因素方面为渐近扩展的恒定系数提供了明确的公式。该证明将抽象的维也纳空间中的经典高斯分析与规则性结构理论理论的参数结合在一起。作为一种成分，我们证明GPAM（扩展）相功能中的最小值不仅具有Cameron-Martin的规律性。
This article resumes the analysis of precise Laplace asymptotics for the generalised Parabolic Anderson Model (gPAM) initiated by Peter Friz and the author. More precisely, we provide an explicit formula for the constant coefficient in the asymptotic expansion in terms of traces and Carleman-Fredholm determinants of certain explicit operators. The proof combines classical Gaussian analysis in abstract Wiener spaces with arguments from the theory of regularity structures. As an ingredient, we prove that the minimiser in the (extended) phase functional of gPAM has better than just Cameron-Martin regularity.
