Stationary Solutions of SPDEs and Infinite Horizon BDSDEs with Non-Lipschitz Coefficients

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dc.creatorZhang, Qi
dc.creatorZhao, Huaizhong
dc.date2008-09-30
dc.date.accessioned2026-07-07T10:06:22Z
dc.date.available2026-07-07T10:06:22Z
dc.descriptionWe prove a general theorem that the $L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{1}})\otimes L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solution of an infinite horizon backward doubly stochastic differential equation, if exists, gives the stationary solution of the corresponding stochastic partial differential equation. We prove the existence and uniqueness of the $L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{1}})\otimes L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solutions for backward doubly stochastic differential equations on finite and infinite horizon with linear growth without assuming Lipschitz conditions, but under the monotonicity condition. Therefore the solution of finite horizon problem gives the solution of the initial value problem of the corresponding stochastic partial differential equations, and the solution of the infinite horizon problem gives the stationary solution of the SPDEs according to our general result.
dc.identifierhttps://arxiv.org/abs/0809.5089
dc.identifierhttp://arxiv.org/abs/0809.5089
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170299
dc.subjectProbability
dc.subjectDynamical Systems
dc.subject60H15; 60H10; 37H10
dc.titleStationary Solutions of SPDEs and Infinite Horizon BDSDEs with Non-Lipschitz Coefficients
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