ANOTHER LOOK INTO THE WONG-ZAKAI THEOREM FOR STOCHASTIC HEAT EQUATION

• 成果类型: Article
• 署名作者: Gu, Yu; Tsai, Li-Cheng
• 署名单位: Carnegie Mellon University; Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1474
• 发表日期: 2019
• 页码: 3037-3061
• 关键词: convergence; limit

摘要

For the heat equation driven by a smooth, Gaussian random potential: partial derivative(t)u(epsilon) = 1/2 Delta u epsilon + u(epsilon) (xi(epsilon) - c(epsilon)), t > 0, chi is an element of R, where xi(e) converges to a spacetime white noise, and c(epsilon) is a diverging constant chosen properly, we prove that u(epsilon) converges in L-n to the solution of the stochastic heat equation for any n >= 1. Our proof is probabilistic, hence provides another perspective of the general result of Hairer and Pardoux (J. Math. Soc. Japan 67 (2015) 1551-1604), for the special case of the stochastic heat equation. We also discuss the transition from homogenization to stochasticity.