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May 2012 Homogenization of a singular random one-dimensional PDE with time-varying coefficients
Étienne Pardoux, Andrey Piatnitski
Ann. Probab. 40(3): 1316-1356 (May 2012). DOI: 10.1214/11-AOP650

Abstract

In this paper we study the homogenization of a nonautonomous parabolic equation with a large random rapidly oscillating potential in the case of one-dimensional spatial variable. We show that if the potential is a statistically homogeneous rapidly oscillating function of both temporal and spatial variables, then, under proper mixing assumptions, the limit equation is deterministic, and convergence in probability holds. To the contrary, for the potential having a microstructure only in one of these variables, the limit problem is stochastic, and we only have convergence in law.

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Étienne Pardoux. Andrey Piatnitski. "Homogenization of a singular random one-dimensional PDE with time-varying coefficients." Ann. Probab. 40 (3) 1316 - 1356, May 2012. https://doi.org/10.1214/11-AOP650

Information

Published: May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1255.60108
MathSciNet: MR2962093
Digital Object Identifier: 10.1214/11-AOP650

Subjects:
Primary: 60H25 , 74Q10 , 80M40

Keywords: large potential , random operator , Stochastic homogenization

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 3 • May 2012
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