In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible ...In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.展开更多
This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost function...This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.展开更多
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string...This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11401091)Postdoctoral Scientific Research Project of Jilin Province(Grant No.RB201357)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.14QNJJ002)China Postdoctoral Science Foundation(Grant No.2014M551152)the China Scholarship Council
文摘In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.
基金supported by the National Natural Science Foundation of China under Grant Nos.11471051 and 11371362the Teaching Mode Reform Project of BUPT under Grant No.BUPT2015JY52+5 种基金supported by the National Natural Science Foundation of China under Grant No.11371029the Natural Science Foundation of Anhui Province under Grant No.1508085JGD10supported by the National Natural Science Foundation of China under Grant No.71373043the National Social Science Foundation of China under Grant No.14AZD121the Scientific Research Project Achievement of UIBE NetworkingCollaboration Center for China’s Multinational Business under Grant No.201502YY003A
文摘This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.
基金supported by National Natural Science Foundation of China(Grant No.91130005)the US Army Research Office(Grant No.W911NF-11-1-0101)
文摘This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.
