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

Laurent Denis | Zendy; Anis Matoussi | Zendy; Lucreţiu Stoica | Zendy

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

Author(s) -

Laurent Denis,

Anis Matoussi,

Lucreţiu Stoica

Publication year - 2009

Publication title -

electronic journal of probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.666

H-Index - 53

ISSN - 1083-6489

DOI - 10.1214/ejp.v14-629

Subject(s) - mathematics , mathematical proof , maximum principle , type (biology) , boundary (topology) , mathematical analysis , comparison theorem , pure mathematics , mathematical optimization , geometry , ecology , biology , optimal control

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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