## The Annals of Probability

### Intermittency-Type Estimates for Some Nondegenerate SPDE'S

Richard B. Sowers

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 23, Number 4 (1995), 1853-1874.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176987806

Digital Object Identifier
doi:10.1214/aop/1176987806

Mathematical Reviews number (MathSciNet)
MR1379171

Zentralblatt MATH identifier
0852.60070

JSTOR