AN APPROXIMATION RESULT FOR A CLASS OF STOCHASTIC HEAT EQUATIONS WITH COLORED NOISE

• 成果类型: Article
• 署名作者: Foondun, Mohammud; Joseph, Mathew; Li, Shiu-Tang
• 署名单位: University of Strathclyde; University of Sheffield; Utah System of Higher Education; University of Utah
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1376
• 发表日期: 2018
• 页码: 2855-2895
• 关键词: chaotic character; asymptotics; driven

摘要

We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier works of [Stoch. Stoch. Rep. 37 (1991) 225-245] and [Ann. Probab. 45 (2017) 377403] among others. Among other things, our results enable us to obtain sharp estimates on the moments of the solution. A main technical ingredient of our method is a local limit theorem which is of independent interest.