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.
Bo Zhu. Baoyan Han. "Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations." J. Appl. Math. 2012 1 - 17, 2012. https://doi.org/10.1155/2012/582645