Abstract
A general type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a method of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.
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(Communicated by Xing-ming GUO)
Project supported by the National Natural Science Foundation of China (No. 10771122), the Natural Science Foundation of Shandong Province of China (No. Y2006A08), and the National Basic Research Program of China (973 Program) (No. 2007CB814900)
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Zhu, Qf., Shi, Yf. & Gong, Xj. Solutions to general forward-backward doubly stochastic differential equations. Appl. Math. Mech.-Engl. Ed. 30, 517–526 (2009). https://doi.org/10.1007/s10483-009-0412-x
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DOI: https://doi.org/10.1007/s10483-009-0412-x