2021/10/20 by Paul Gassiat, Gassiat, Paul, Benjamin Seeger +1
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Stochastic processes and financial applications #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.2110.10337
We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set on a sub-domain with Neumann boundary conditions. Under a convexity assumption on the domain, we obtain a comparison theorem which yields existence and uniqueness of solutions as well as continuity with respect to the driving noise. As an application, we study the long time behaviour of a stochastically perturbed mean-curvature flow in a cylinder-like domain with right angle contact boundary condition.