## Annals of Probability

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

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

Gopinath Kallianpur and Jie Xiong

#### 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

**Permanent link to this document**

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