Pathwise stationary solutions of stochastic differential equations and backward doubly stochastic differential equations on infinite horizon
Pathwise stationary solutions of stochastic differential equations and backward doubly stochastic differential equations on infinite horizon
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发表时间：
2006
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通讯作者：
Qi S. Zhang;Huaizhong Zhao
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作者：
Qi S. Zhang;Huaizhong Zhao
本文的主要目的是研究随机偏微分方程平稳解的存在性。我们在无限时间范围内的后向双随机微分方程与 SPDE 的平稳解之间建立了新的联系。为此，我们研究了无限时间范围内相关 BDSDE 解的存在性，并证明它是相应 SPDE 的平稳粘度解。
The main purpose of this paper is to study the existence of stationary solution for stochastic partial differential equations. We establish a new connection between backward doubly stochastic differential equations on infinite time horizon and the stationary solution of the SPDEs. For this we study the existence of the solution of the associated BDSDEs on infinite time horizon and prove it is a stationary viscosity solution of the corresponding SPDEs.