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In this article, we consider the solvability problems for the fully coupled forward-backward stochastic difference equations (FBSΔEs). On one hand, we provide the necessary and sufficient condition for the solvability of the linear FBSΔEs. On the other hand, under the assumption that the coefficients satisfy the monotonicity condition, we investigate the existence and uniqueness theorems for the general non linear FBSΔEs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the solvability problems for the fully coupled forward–backward stochastic difference equations (FBSΔEs) on spaces related to discrete time, finite state processes. On one hand, we provide the necessary and sufficient condition for the solvability of the linear FBSΔEs. On the other hand, under the assumption that the coefficients satisfy the monotonicity condition, we investigate the existence and uniqueness theorems for the general nonlinear FBSΔEs. [ABSTRACT FROM AUTHOR]

In this paper, we study the maximum principle for stochastic optimal control problems of forward–backward stochastic difference systems (FBSΔSs). Two types of FBSΔSs are investigated. The first one is described by a partially coupled forward–backward stochastic difference equation (FBSΔE) and the second one is described by a fully coupled FBSΔE. By adopting an appropriate representation of the product rule and an appropriate formulation of the adjoint process, we deduce the adjoint difference equation. Finally, the maximum principle for this optimal control problem with the control domain being convex is established. [ABSTRACT FROM AUTHOR]

This paper explores the relationship between non-Markovian fully coupled forward–backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional Itô calculus. Under mild hypotheses, we prove that the forward–backward stochastic system provides the unique classical solution to the path-dependent PDE. [ABSTRACT FROM AUTHOR]

In this paper, we study the minimum mean square estimator for non-bounded random variables under sublinear operators. The existence and uniqueness of the minimum mean square estimator are obtained. Several properties of the minimum mean square estimator for non-bounded random variables are proved under some mild assumptions. [ABSTRACT FROM AUTHOR]