## The Annals of Probability

- Ann. Probab.
- Volume 45, Number 1 (2017), 377-403.

### Strong invariance and noise-comparison principles for some parabolic stochastic PDEs

Mathew Joseph, Davar Khoshnevisan, and Carl Mueller

#### Abstract

We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.

#### Article information

**Source**

Ann. Probab., Volume 45, Number 1 (2017), 377-403.

**Dates**

Received: April 2014

Revised: January 2015

First available in Project Euclid: 26 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1485421335

**Digital Object Identifier**

doi:10.1214/15-AOP1009

**Mathematical Reviews number (MathSciNet)**

MR3601652

**Zentralblatt MATH identifier**

1367.60082

**Subjects**

Primary: 60H15: Stochastic partial differential equations [See also 35R60]

Secondary: 35K57: Reaction-diffusion equations

**Keywords**

Stochastic PDEs comparison theorems white noise

#### Citation

Joseph, Mathew; Khoshnevisan, Davar; Mueller, Carl. Strong invariance and noise-comparison principles for some parabolic stochastic PDEs. Ann. Probab. 45 (2017), no. 1, 377--403. doi:10.1214/15-AOP1009. https://projecteuclid.org/euclid.aop/1485421335