## Electronic Journal of Probability

- Electron. J. Probab.
- Volume 22 (2017), paper no. 68, 32 pp.

### Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem

Ajay Chandra and Hao Shen

#### Abstract

Upon its inception the theory of regularity structures [7] allowed for the treatment for many semilinear perturbations of the stochastic heat equation driven by space-time white noise. When the driving noise is non-Gaussian the machinery of the theory can still be used but must be combined with an infinite number of stochastic estimates in order to compensate for the loss of hypercontractivity, as was done in [12]. In this paper we obtain a more streamlined and automatic set of criteria implying these estimates which facilitates the treatment of some other problems including non-Gaussian noise such as some general phase coexistence models [13], [16] - as an example we prove here a generalization of the Wong-Zakai Theorem found in [10].

#### Article information

**Source**

Electron. J. Probab., Volume 22 (2017), paper no. 68, 32 pp.

**Dates**

Received: 1 May 2016

Accepted: 18 July 2017

First available in Project Euclid: 9 September 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ejp/1504922531

**Digital Object Identifier**

doi:10.1214/17-EJP84

**Mathematical Reviews number (MathSciNet)**

MR3698737

**Zentralblatt MATH identifier**

1379.60064

**Subjects**

Primary: 60H15 Stochastic Partial Differential Equations

**Keywords**

stochastic partial differential equations regularity structures

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Chandra, Ajay; Shen, Hao. Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem. Electron. J. Probab. 22 (2017), paper no. 68, 32 pp. doi:10.1214/17-EJP84. https://projecteuclid.org/euclid.ejp/1504922531