One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, ...One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".展开更多
The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cone...The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.展开更多
基金National Natural Science Foundation of China ( No. 11171062 ) Natural Science Foundation for the Youth,China ( No.11101077) Innovation Program of Shanghai Municipal Education Commission,China ( No. 12ZZ063)
文摘One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".
基金This work has been supported by US Army Research Office Grant(No.W911NF-15-1-0223)The Scientific and Technological Research Council of Turkey Grant(No.1059B191300653).
文摘The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.
