Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations

Abstract EN

We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values.

We also show continuous dependence theorem and convergence theorem for this kind of equations.

A probabilistic interpretation for solutions to a class of stochastic partial differential equations is given.