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Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (4): 1084-1092.

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Forward-Backward Doubly Stochastic Differential Equations

(1.Statistics and Mathematics College, Shandong University of Finance, Jinan 250014, 2.School of Mathematics, Shandong University, Jinan 250100)

Received:2007-07-14 Revised:2008-11-20 Online:2009-08-25 Published:2009-08-25
Supported by:
国家自然科学基金(10771122)、山东省自然科学基金(Y2006A08)和国家重点基础研究发展计划(2007CB814900)资助

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Abstract

Abstract:

A type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. Under some natural monotonicity assumptions, the existence and uniqueness result is established.

Key words: Forward-backward doubly stochastic differential equations, Equivalent norm, Contraction mapping

CLC Number:

60H10

Cite this article

ZHU Qing-Feng, SHI Yu-Feng. Forward-Backward Doubly Stochastic Differential Equations[J].Acta mathematica scientia,Series A, 2009, 29(4): 1084-1092.

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References

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[2] Pardoux E, Peng S. Backward doubly stochastic differential equations and systems of quasilinear parabolic SPDEs. Probab Theory Relat Fields, 1994, 98: 209--227

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[4] Feyel D. Sur la m\'{e}thode de Picard (EDO et EDS). in S\'{e} minaire de Probabilit\'{e}s XXI, Lecture Notes in Mathematics, 1247: 515--519

[5] Pardoux E, Tang S. Forward-backward stochastic differential equations and quasilinear parabolic PDEs. Probab Theory Relat Fields, 1999, 114: 123--150

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