The Annals of Probability

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

Mathew Joseph, Davar Khoshnevisan, and Carl Mueller

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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


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