STRONG INVARIANCE AND NOISE-COMPARISON PRINCIPLES FOR SOME PARABOLIC STOCHASTIC PDES

• 成果类型: Article
• 署名作者: Joseph, Mathew; Khoshnevisan, Davar; Mueller, Carl
• 署名单位: University of Sheffield; Utah System of Higher Education; University of Utah; University of Rochester
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1009
• 发表日期: 2017
• 页码: 377-403
• 关键词: partial-differential-equations; intermittence; spdes

摘要

We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.