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Intermittency-Type Estimates for Some Nondegenerate SPDE'S

Richard B. Sowers
The Annals of Probability
Vol. 23, No. 4 (Oct., 1995), pp. 1853-1874
Stable URL: http://www.jstor.org/stable/2244818
Page Count: 22
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Intermittency-Type Estimates for Some Nondegenerate SPDE'S
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Abstract

In this paper we prove some intermittency-type estimates for the stochastic partial differential equation du = Lu dt + Mlu⚬ dWl t, where L is a strongly elliptic second-order partial differential operator and the Ml's are first-order partial differential operators. Here the Wl's are standard Wiener processes and ⚬ denotes Stratonovich integration. We assume for simplicity that $u(0,\cdot) \equiv 1$. 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 (p2t)-1logE[|u(t,x)|p] as t, then p, become large.

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