2013/01/07 by Denis Laurent, Matoussi Anis, Laurent, Denis +5 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #31B150 #35R60 #60H15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:31B150 #msc:35R60 #msc:60H15
paper · pdf · doi:10.48550/arxiv.1301.1221
19 pages. arXiv admin note: substantial text overlap with arXiv:1202.3296, arXiv:1210.3445, arXiv:1201.1092
arxiv created 2013/01/07 · openalex publication_date 2013/01/07 · arxiv updated 2013/01/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove the existence and uniqueness of solution of the obstacle problem for quasilinear Stochastic PDEs with non-homogeneous second order operator. Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u,ν) where u is a predictable continuous process which takes values in a proper Sobolev space and ν is a random regular measure satisfying minimal Skohorod condition. Moreover, we establish a maximum principle for local solutions of such class of stochastic PDEs. The proofs are based on a version of Itô's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.