2018/04/23 by Yuchao Dong, Xue Yang, Dong, Yuchao +3
Economics, Econometrics and Finance · Computer Science · Mathematics · #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1804.09051
We prove the existence and uniqueness of solution of the obstacle problem for quasilinear stochastic partial differential equations (OSPDEs for short) with Neumann boundary condition. Our method is based on the analytical technics coming from 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.