On a Monte Carlo scheme for some linear stochastic partial differential equations

Nakagawa Takuya () and Tanaka Akihiro ()
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Nakagawa Takuya: Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan
Tanaka Akihiro: Sumitomo Mitsui Banking Corporation, 1-1-2, Marunouchi, Chiyoda-ku, Tokyo, 100-0005, Japan

Monte Carlo Methods and Applications, 2021, vol. 27, issue 2, 169-193

Abstract: The aim of this paper is to study the simulation of the expectation for the solution of linear stochastic partial differential equation driven by the space-time white noise with the bounded measurable coefficient and different boundary conditions. We first propose a Monte Carlo type method for the expectation of the solution of a linear stochastic partial differential equation and prove an upper bound for its weak rate error. In addition, we prove the central limit theorem for the proposed method in order to obtain confidence intervals for it. As an application, the Monte Carlo scheme applies to the stochastic heat equation with various boundary conditions, and we provide the result of numerical experiments which confirm the theoretical results in this paper.

Keywords: Stochastic partial differential equation; computational method (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/mcma-2021-2088

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