Mathematics – Probability
Scientific paper
2006-02-02
Journal of Functional Analysis,Vol. 252 (2007), 171-219
Mathematics
Probability
Scientific paper
10.1016/j.jfa.2007.06.019
In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between $L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{1}}) \otimes L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. Moreover, we prove the existence and uniqueness of the solutions of BDSDEs on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary solutions (independent of any initial value) of SPDEs. The connection of the weak solutions of SPDEs and BDSDEs has independent interests in the areas of both SPDEs and BSDEs.
Zhang Qian
Zhao Huaizhong
No associations
LandOfFree
Stationary Solutions of SPDEs and Infinite Horizon BDSDEs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stationary Solutions of SPDEs and Infinite Horizon BDSDEs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stationary Solutions of SPDEs and Infinite Horizon BDSDEs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-485119