On the continuity of the probabilistic representation of a semilinear Neumann–Dirichlet problem

Lucian Maticiuc and Aurel Răşcanu

Stochastic Processes and their Applications, 2016, vol. 126, issue 2, 572-607

Abstract: In this article we prove the continuity of the deterministic function u:[0,T]×D̄→R, defined by u(t,x):=Ytt,x, where the process (Yst,x)s∈[t,T] is given by the generalized multivalued backward stochastic differential equation:{−dYst,x+∂φ(Yst,x)ds+∂ψ(Yst,x)dAst,x∋f(s,Xst,x,Yst,x)ds+g(s,Xst,x,Yst,x)dAst,x−Zst,xdWs,t≤sKeywords: Feynman–Kac formula; Reflected diffusion processes; Continuity w.r.t. initial data; Neumann–Dirichlet boundary conditions (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.09.011

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