POLARITY OF ALMOST ALL POINTS FOR SYSTEMS OF NONLINEAR STOCHASTIC HEAT EQUATIONS IN THE CRITICAL DIMENSION

• 成果类型: Article
• 署名作者: Dalang, Robert C.; Mueller, Carl; Xiao, Yimin
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Michigan State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1516
• 发表日期: 2021
• 页码: 2573-2598
• 关键词: trajectories

摘要

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, partial derivative/partial derivative t u(t, x) = partial derivative(2)/partial derivative x(2) u(t, x) + sigma (u(t, x)(W) over dot (t, x). Here, t >= 0, x is an element of R and (W) over dot (t, x) is an R-d-valued space-time white noise. We say that a point z is an element of R-d is polar if P{u(t, x) = z for some t > 0 and x is an element of R} = 0. We show that, in the critical dimension d = 6, almost all points in R-d are polar.