Stochastic PDEs and infinite horizon backward doubly stochastic differential equations

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. © 2012 bo zhu and baoyan han.