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October, 1995 Intermittency-Type Estimates for Some Nondegenerate SPDE'S
Richard B. Sowers
Ann. Probab. 23(4): 1853-1874 (October, 1995). DOI: 10.1214/aop/1176987806


In this paper we prove some intermittency-type estimates for the stochastic partial differential equation $du = \mathscr{L}u dt + \mathscr{M}_lu\circ dW^l_t$, where $\mathscr{L}$ is a strongly elliptic second-order partial differential operator and the $\mathscr{M}_l$'s are first-order partial differential operators. Here the $W^l$'s are standard Wiener processes and $\circ$ denotes Stratonovich integration. We assume for simplicity that $u(0,\cdot) \equiv 1$. Our interest here is the behavior of $\mathbb{E}\lbrack|u(t,x)|^p\rbrack$ for large time and large $p$; more specifically, our interest is the growth of $(p^2t)^{-1}\log\mathbb{E}\lbrack|u(t,x)|^p\rbrack$ as $t$, then $p$, become large.


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Richard B. Sowers. "Intermittency-Type Estimates for Some Nondegenerate SPDE'S." Ann. Probab. 23 (4) 1853 - 1874, October, 1995.


Published: October, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0852.60070
MathSciNet: MR1379171
Digital Object Identifier: 10.1214/aop/1176987806

Primary: 60H15
Secondary: 47D07 , 60G60 , 76W05 , 93E11

Keywords: Intermittency , moment Lyapunov functions , Stochastic partial differential equations

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 4 • October, 1995
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