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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Forward-backward stochastic differential equations with mixed initial-terminal conditions


Author: Jiongmin Yong
Journal: Trans. Amer. Math. Soc. 362 (2010), 1047-1096
MSC (2000): Primary 60H10
Published electronically: September 9, 2009
MathSciNet review: 2551515
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Abstract: Well-posedness of forward-backward stochastic differential equations (FBSDEs, for short) in $ L^p$ spaces with mixed initial-terminal conditions is studied. A notion of Lyapunov operator is introduced, whose existence leads to a priori estimates of the adapted solutions sufficient for the well-posedness of the corresponding FBSDEs, via the method of continuation. Various situations are discussed under which Lyapunov operators do exist.


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Additional Information

Jiongmin Yong
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: jyong@mail.ucf.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04896-X
Keywords: Forward-backward stochastic differential equations, mixed initial-terminal conditions, Lyapunov operator, method of continuation
Received by editor(s): December 28, 2007
Received by editor(s) in revised form: August 1, 2008
Published electronically: September 9, 2009
Additional Notes: This work was supported in part by the NSF grant DMS-0604309.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.