Stochastic heat equation with Ornstein–Uhlenbeck operator

Xiang Li

Statistics & Probability Letters, 2023, vol. 201, issue C

Abstract: We study the stochastic partial differential equation ∂u∂t=Lu+uẆ in Skorohod sense, where L is the generator of a one-dimensional Ornstein–Uhlenbeck (OU) process X and Ẇ is a (1+1)-dimensional space–time white noise. We follow the method established in Hu and Nualart (2009) to prove a Feynman–Kac type representation of the moments of solution. Through this representation, we use the method established in Chen (2015) and a large deviation principle of OU process to obtain an intermittency result.

Keywords: Stochastic partial differential equation; Ornstein–Uhlenbeck operator; Feynman–Kac representations; Intermittency (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109887

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