Backward doubly stochastic differential equations with infinite time horizon.
type: Item
instance of: scholarly article
title: Backward doubly stochastic differential equations with infinite time horizon.
zbMATH Open document ID: 1274.60193
author: Bo Zhu
author: Baoyan Han
published in: Applications of Mathematics
publication date: 2013-03-21T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/143008
review text: In the paper, a class of infinite horizon backward doubly stochastic differential equations (BDSDEs) is studied. The existence and uniqueness of the solution is proved using a standard fixed point argument under (global in space, local in time) Lipschitz assumptions. The assumption of exponential decay of the solution (see, e.g., [\textit{Q. Zhang} and \textit{H. Zhao}, J. Funct. Anal. 252, No. 1, 171--219 (2007; Zbl 1127.60059)]) is replaced by assuming a square integrable terminal condition. The next result is a proof of continuous dependence on the terminal condition of the solution couple and a convergence result for the solutions to the BDSDEs for different terminal conditions converging in mean square. Finally, the last result is used to demonstrate the relation between finite and infinite time horizon BDSDEs.
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 6147980
zbMATH Keywords: infinite time horizon
zbMATH Keywords: backward doubly stochastic differential equations
zbMATH Keywords: filtration
zbMATH Keywords: backward stochastic integral
MaRDI profile type: Publication
OpenAlex ID: W2060403488
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DOI: 10.1007/S10492-012-0039-2
description: scientific article; zbMATH DE number 6147980