Forward-backward doubly stochastic differential equations and related stochastic partial differential equations (Q1934378)

The authors prove that classes of systems of coupled forward-backward doubly stochastic differential equations (FBDSDEs) may have the same unique solvability if they are linked by appropriate bridges. Their argumentation allows a ``probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential equations (SPDEs) combined with algebraic equations''. The analysis is based on a coupling of forward and backward components of related FBDSDEs.