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- Publisher
- Springer Journals
- Copyright
- Copyright © 2006 by Birkhäuser Verlag, Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-006-0263-x
- Publisher site
- See Article on Publisher Site
Abstract
This paper is devoted to forward-backward systems of stochastic differential equations in which the forward equation is not coupled to the backward one, both equations are infinite dimensional and on the time interval (0, + ∞). The forward equation defines an Ornstein-Uhlenbeck process, the driver of the backward equation has a linear part which is the generator of a strongly continuous, dissipative, compact semigroup, and a nonlinear part which is assumed to be continuous with linear growth. Under the assumption of equivalence of the laws of the solution to the forward equation, we prove the existence of a solution to the backward equation. We apply our results to a stochastic game problem with infinitely many players.
Journal
Journal of Evolution Equations – Springer Journals
Published: Aug 1, 2006