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A variational formula for controlled backward stochastic partial differential equations and some application

A variational formula for controlled backward stochastic partial differential equations and some application
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摘要 An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established. An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.
出处 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第3期295-306,共12页 高校应用数学学报(英文版)(B辑)
基金 Supported by the National Natural Science Foundation of China(11101140,11301177) the China Postdoctoral Science Foundation(2011M500721,2012T50391) the Zhejiang Natural Science Foundation of China(Y6110775,Y6110789)
关键词 Variational formula stochastic evolution equation backward stochastic evolution equation stochastic maximum principle spike variation. Variational formula, stochastic evolution equation, backward stochastic evolution equation,stochastic maximum principle, spike variation.
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  • 1Pontryagin L S, Boltyanskti V G, Camkrelidze R V, Mischenko E F. The Mathematical Theory of Optimal Control Processes. New York: John Wiley, 1962.
  • 2Bensoussan A. Lectures on stochastic control. In: Lecture Notes in Mathematics, 972, Berlin: Springer- Verlag, 1982.
  • 3Bismut J M. An introductory approach to duality in optimal stochastic control. SIAM journal on Control and Optimization, 1978, 20:62-78.
  • 4Kushner H J. Necessary conditions for continuous parameter stochastic optimization problems. SIAM Journal on Control and Optimization, 1972, 10:550-565.
  • 5Peng S. A general stochastic maximum principle for optimal control problems. SIAM Journal on Control and Optimization, 1990, 28:966-979.
  • 6Peng S. Backward stochastic differential equations and application to optimal control. Applied Mathematics and Optimization, 1993, 27(4): 125-144.
  • 7Xu W S. Stochastic maximum principle for optimal control problem of forward and backward system. Journal of Australian Mathematical Society, 1995, B(37): 172-185.
  • 8Ma J, Protter P, Yong J. Solving forward-backward stochastic differential equations explicitly-a four step scheme. Probability Theory and Related Fields, 1994, 98:339-359.
  • 9Hu Y, Peng S. Solution of a forward-backward stochastic differential equations. Probability Theory and Related Fields, 1995, 103:273-283.
  • 10Peng S, Wu Z. Fully coupled forward-backward stochastic differential equations and applications to the optimal control. SIAM Journal on Control and Optimization, 1999, 37(3): 825-843.

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