Maximum Principle and Comparison Theorem for Quasi-linear Stochastic PDE's

Laurent Denis (Université d'Evry Val d'Essonne)
Anis Matoussi (Université du Maine)
Lucretiu Stoica (University of Bucharest)

Abstract


We prove a comparison theorem and maximum principle for a local solution of quasi-linear parabolic stochastic PDEs, similar to the well known results in the deterministic case. The proofs are based on a version of Ito's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary. Moreover we shortly indicate how these results generalize for Burgers type SPDEs

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Pages: 500-530

Publication Date: February 23, 2009

DOI: 10.1214/EJP.v14-629

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