MOMENT ESTIMATES FOR SOME RENORMALIZED PARABOLIC ANDERSON MODELS

• 成果类型: Article
• 署名作者: Chen, Xia; Deya, Aurelien; Ouyang, Cheng; Tindel, Samy
• 署名单位: University of Tennessee System; University of Tennessee Knoxville; Universite de Lorraine; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Purdue University System; Purdue University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1517
• 发表日期: 2021
• 页码: 2599-2636
• 关键词: stochastic heat-equation; chaotic character; asymptotics; noise; SPACE; driven; rough

摘要

The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: partial derivative(t)u(t) (x) = 1/2 Delta u(t) (x) + u(t) (x). (W) over dot (x), for t is an element of R+ and x is an element of R-d, where (W) over dot (x) is a Gaussian noise whose space time covariance function is singular. In this rough context we shall give some information about the moments of u(t) (x) when the stochastic heat equation is interpreted in the Skorohod as well as the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.