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, + infinity). 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.
Infinite horizon BSDEs in infinite dimensions with continuous driver and applications / M. Fuhrman, Y. Hu. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 6:3(2006), pp. 459-484.
|Titolo:||Infinite horizon BSDEs in infinite dimensions with continuous driver and applications|
|Parole Chiave:||backward stochastic differential equations; stochastic equations in infinite dimensional spaces; stochastic differential games|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2006|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00028-006-0263-x|
|Appare nelle tipologie:||01 - Articolo su periodico|
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