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
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.