Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients
By Qi S. Zhang, Huaizhong Zhao. 2006
78 citations recorded by the source corpus.
Abstract We prove a general theorem that the L ρ 2 ( R d ; R 1 ) ⊗ L ρ 2 ( R d ; 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 ( R d ; R 1 ) ⊗ L ρ 2 ( R d ; 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.
Subfields: Applied Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/397dcb10f121252b04fff6a6b385dd44df9f71fc
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Citations in the corpus
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