Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System
Pure and Applied Mathematics Journal
Volume 4, Issue 3, June 2015, Pages: 101-108
Received: Apr. 22, 2015;
Accepted: May 5, 2015;
Published: Jun. 1, 2015
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Hong Zhang, School of Information, Beijing Wuzi University, Beijing, China
Jingyi Wang, School of Banking and Finance, University of International Business and Economics, Beijing, China
Tengyu Zhao, School of Management Science and Engineering, Central University of Finance and Economics, Beijing, China
Li Zhou, School of Information, Beijing Wuzi University, Beijing, China
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Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.
Mean-Field Backward Doubly, Stochastic System, Stochastic Control
To cite this article
Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System, Pure and Applied Mathematics Journal.
Vol. 4, No. 3,
2015, pp. 101-108.
A. Szukala, A Knese-type theorem for euqation x=f (t, x) in locally convex spaces, Journal for analysis and its applications, 18 (1999), 1101-1106.
M. Tang and Q. Zhang, Optimal variational principle for backward stochastic control systems associated with Levy processes, Sci China Math, 55 (2012), 745-761.
SevaS. Tang and X. Li, Necessary condition for optimal control of stochastic systems with random jumps, SIAM J Control Optim, 32 (1994), 1447-1475.
J. Valero, On the kneser property for some parapolic problems, Topology and its applicanons, 155 (2005), 975-989.
Z. Wu, Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems, J. Systems Sci. Math. Sci., 11 (1998), 249-259.
Z. Wu, Forward-backward stochastic differential equations with Brownian Motion and Process Poisson, Acta Math. Appl. Sinica, English Series, 15 (1999), 433-443.
Z. Wu, A maximum principle for partially observed optimal control of forward-backward stochastic control systems, Sci China Ser F, 53 (2010), 2205-2214.
Z. Wu and Z. Yu, Fully coupled forward-backward stochastic differential equations and related partial differential equations system, Chinese Ann Math Ser A, 25 (2004), 457-468
H. Xiao and G. Wang, A necessary condition for optimal control of initial coupled forward-backward stochastic differential equations with partial information, J. Appl. Math. Comput., 37 (2011), 347-359.
J. Xiong, An Introduction to Stochastic Filtering Theory, London, U.K.: Oxford University Press, 2008.