Maximum principle for quasilinear SPDE's on a bounded domain without regularity assumptions

2012/01/05 by Laurent Denis, Denis, Laurent, Anis Matoussi +1 · 2 citations
Mathematics · #35R60 #60G46 #60H15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:35R60 #msc:60G46 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1201.1092

arxiv created 2012/08/31 · arxiv updated 2012/09/03

Abstract

We prove a maximum principle for local solutions of quasi-linear parabolic stochastic PDEs, with non-homogeneous second order operator on a bounded domain and driven by a space-time white noise. Our method based on an approximation of the domain and the coefficients of the operator, does not require regularity assumptions. As in previous works, the results are consequences of Itô's formula and estimates for the positive part of local solutions which are non-positive on the lateral boundary.

Cited by

• Stochastic PDEs driven by G-Brownian motion and the associated Backward Doubly Stochastic Differential Equations
• The Obstacle Problem for Quasilinear Stochastic PDEs with non-homogeneous operator

Related

• Maximum Principle for Quasilinear Stochastic PDEs with Obstacle
• Maximum Principle for Quasi-linear Backward Stochastic Partial Differential Equations
• A regularity result for quasilinear stochastic partial differential equations of parabolic type
• The Obstacle Problem for Quasilinear Stochastic PDEs with non-homogeneous operator
• Maximum Principle for Quasi-linear Reflected Backward SPDEs