Stationary solutions of SPDEs and infinite horizon BDSDEs |
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Authors: | Qi Zhang Huaizhong Zhao |
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Affiliation: | a Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK b School of Mathematics and System Sciences, Shandong University, Jinan 250100, China |
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Abstract: | In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between 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 (independent of any initial value) of SPDEs. The connection of the weak solutions of SPDEs and BDSDEs has independent interests in the areas of both SPDEs and BSDEs. |
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Keywords: | Backward doubly stochastic differential equations Weak solutions Stochastic partial differential equations Stationary solution Random dynamical systems |
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