Stationary Solutions of SPDEs and Infinite Horizon BDSDEs

  title={Stationary Solutions of SPDEs and Infinite Horizon BDSDEs},
  author={Qi Zhang and Huaizhong Zhao},
In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between Lρ(R; R)⊗Lρ(R; R) valued solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. Moreover, we prove the existence and uniqueness of the solutions of BDSDEs on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary solutions… CONTINUE READING
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