## Bernoulli

- Bernoulli
- Volume 24, Number 1 (2018), 354-385.

### Large deviations for stochastic heat equation with rough dependence in space

Yaozhong Hu, David Nualart, and Tusheng Zhang

#### Abstract

In this paper, we establish a large deviation principle for the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter $H\in (\frac{1}{4},\frac{1}{2})$ in the space variable.

#### Article information

**Source**

Bernoulli, Volume 24, Number 1 (2018), 354-385.

**Dates**

Received: September 2015

Revised: June 2016

First available in Project Euclid: 27 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1501142447

**Digital Object Identifier**

doi:10.3150/16-BEJ880

**Mathematical Reviews number (MathSciNet)**

MR3706761

**Zentralblatt MATH identifier**

1379.60069

**Keywords**

fractional Brownian motion large deviations stochastic heat equation

#### Citation

Hu, Yaozhong; Nualart, David; Zhang, Tusheng. Large deviations for stochastic heat equation with rough dependence in space. Bernoulli 24 (2018), no. 1, 354--385. doi:10.3150/16-BEJ880. https://projecteuclid.org/euclid.bj/1501142447