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2009 Maximum Principle and Comparison Theorem for Quasi-linear Stochastic PDE's
Laurent Denis, Anis Matoussi, Lucretiu Stoica
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Electron. J. Probab. 14: 500-530 (2009). DOI: 10.1214/EJP.v14-629


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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Laurent Denis. Anis Matoussi. Lucretiu Stoica. "Maximum Principle and Comparison Theorem for Quasi-linear Stochastic PDE's." Electron. J. Probab. 14 500 - 530, 2009.


Accepted: 23 February 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60050
MathSciNet: MR2480551
Digital Object Identifier: 10.1214/EJP.v14-629

Primary: 60H15
Secondary: 35R60 , 60G46

Keywords: Ito's formula , maximum principle , Moser's iteration , Stochastic partial differential equation

Vol.14 • 2009
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