Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients |
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Authors: | Qi Zhang Huaizhong Zhao |
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Institution: | 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: | We prove a general theorem that the -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 -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. |
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Keywords: | 60H15 60H10 37H10 |
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