The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations
Pure and Applied Mathematics Journal
Volume 4, Issue 3, June 2015, Pages: 120-127
Received: May 14, 2015;
Accepted: May 26, 2015;
Published: Jun. 6, 2015
Views 4002 Downloads 103
Jie Zhu, School of Information, Beijing Wuzi University, Beijing, China
Hong Zhang, School of Information, Beijing Wuzi University, Beijing, China
Li Zhou, School of Information, Beijing Wuzi University, Beijing, China
Yuhang Feng, Insurance Department, Central University of Finance and Economics, Beijing, China
Since 1990 Pardoux and Peng, proposed the theory of backward stochastic differential equation Backward stochastic differential equation and is backward stochastic differential equations (short for FBSDE) theory has been widely research (see El Karoui, Peng and Cauenez, Ma and Yong, etc.) Generally, a backward stochastic differential equation is a type Ito stochastic differential equation and a coupling Pardoux - Peng and backward stochastic differential equation. Antonelli, Ma, Protter and Yong is backward stochastic differential equation for a series of research, and apply to the financial. One of the research direction is put forward by Hu and Peng first. Peng and Wu Peng and Shi made a further research, and Yong to a more detailed discussion of this method, by introducing the concept of the bridge, systematically studied the FBSDE continuity method. Because such a system can be applied to random Feynman - Kac of partial differential equations of research, And a double optimal control problem of stochastic control systems, we will be working in Peng and Shi further in-depth study on the basis of this category are backward stochastic differential equation. In this paper, we are considering various constraint conditions with backward stochastic differential equation.
The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations, Pure and Applied Mathematics Journal.
Vol. 4, No. 3,
2015, pp. 120-127.
Deepmala and H. K. Pathak, A study on some problems on existence of solutions for nonlinear functional-integral equations, Acta Mathematica Scientia, 33 B(5) (2013), 1305–1313.
Deepmala, A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications, Ph.D. Thesis (2014), Pt. Ravishankar Shukla University, Raipur (Chhatisgarh) India – 492 010.
V.N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D. Thesis (2007), Indian Institute of Technology, Roorkee - 247 667, Uttarakhand, India.
V.N. Mishra, L.N. Mishra, Trigonometric Approximation of Signals (Functions) in Lp (p _ 1)− norm, International Journal of Contemporary Mathematical Sciences, Vol. 7, 2012, no. 19, pp. 909 – 918.
L.N. Mishra, S.K. Tiwari, V.N. Mishra, I.A. Khan; Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces, Journal of Function Spaces, Volume 2015 (2015), Article ID 960827, 8 pages.
V.N. Mishra, M.L. Mittal, U. Singh, On best approximation in locally convex space, Varahmihir Journal of Mathematical Sciences India, Vol. 6, No.1, (2006), 43-48.
Deepmala, Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming, Int. J. Math. Math. Sci., Vol. 2014, Article ID: 706585, 9 pages.
Deepmala, H.K. Pathak, On Solutions of Some Functional-Integral Equations in Banach Algebra, Research Journal of Science and Technology 5 (3), 358-362.
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. Sonica, 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. Compute, 37 (2011), 347-359.
J. Xiong, An Introduction to Stochastic Filtering Theory, London, U.K.: Oxford University Press, 2008.