Intermittency-type estimates for some nondegenerate SPDE'S

• 成果类型: Article
• 署名作者: Sowers, RB
• 署名单位: University of Southern California
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176987806
• 发表日期: 1995
• 页码: 1853-1874
• 关键词: conditional diffusions

摘要

In this paper we prove some intermittency-type estimates for the stochastic partial differential equation du = L u dt + M(1)u circle dW(t)(l), where L is a strongly elliptic second-order partial differential operator and the M(l)'s are first-order partial differential operators. Here the W-l's are standard Wiener processes and circle denotes Stratonovich integration. We assume for simplicity that u(0, .) equivalent to 1. Our interest here is the behavior of E[\ u(t, x)\(p)] for large time and large p; more specifically, our interest is the growth of (p(2)t)(-1) log E[\ u(t, x)\(p)] as t, then p, become large.