FBSDEs with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity
AbstractWe extend the work of Delong and Imkeller (2010)Â  and  concerning backward stochastic differential equations with time delayed generators (delay BSDEs). We give moment and a priori estimates in general Lp-spaces and provide sufficient conditions for the solution of a delay BSDE to exist in Lp. We introduce decoupled systems of SDEs and delay BSDEs (delay FBSDEs) and give sufficient conditions for their variational differentiability. We connect these variational derivatives to the Malliavin derivatives of delay FBSDEs via the usual representation formulas. We conclude with several path regularity results, in particular we extend the classic L2-path regularity to delay FBSDEs.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 121 (2011)
Issue (Month): 9 (September)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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