JDErevised.pdf (306.38 kB)
Download file

Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients

Download (306.38 kB)
journal contribution
posted on 21.07.2014, 10:18 by Qi Zhang, Huaizhong Zhao
We prove a general theorem that the L (R ; R) ⊗ L (R ; R)-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 (R ; R) ⊗ L (R ; R)-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.

Funding

Q.Z. would like to acknowledge the financial support of the National Basic Research Program of China (973 Program) with Grant No. 2007CB814904.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Differential Equations

Volume

248

Issue

5

Pages

953 - 991

Citation

ZHANG, Q. and ZHAO, H.-Z., 2010. Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients. Journal of Differential Equations, 2010 (5), pp. 953-991.

Publisher

© Elsevier Inc.

Version

AM (Accepted Manuscript)

Publication date

2010

Notes

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Differential Equations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at http://dx.doi.org/10.1016/j.jde.2009.12.013.

ISSN

0022-0396

eISSN

1090-2732

Language

en