## Annals of Probability

### Large deviations for a class of stochastic partial differential equations

#### Abstract

We consider the random fields $X^{\varepsilon}(t, q), \ t\geq 0, \ q\in {\mathcal O},$ goverened by stochastic partial differential equations driven by a Gaussian white noise in space-time, where $\mathcal O$ is a bounded domain in ${\mathbb R}^d$ with regular boundary. To study the continuity of the random fields $X^\varepsilon$ in space and time variables, we prove an analogue of Garsia's theorem. We then derive the large deviation results based on the methods used by the second author in another paper. This article provides an alternative proof of Sower's result for the case of d = 1.

#### Article information

Source
Ann. Probab., Volume 24, Number 1 (1996), 320-345.

Dates
First available in Project Euclid: 15 January 2003

https://projecteuclid.org/euclid.aop/1042644719

Digital Object Identifier
doi:10.1214/aop/1042644719

Mathematical Reviews number (MathSciNet)
MR1387638

Zentralblatt MATH identifier
0854.60026

#### Citation

Kallianpur, Gopinath; Xiong, Jie. Large deviations for a class of stochastic partial differential equations. Ann. Probab. 24 (1996), no. 1, 320--345. doi:10.1214/aop/1042644719. https://projecteuclid.org/euclid.aop/1042644719