In this paper, we mainly investigate the weak convergence analysis about the error terms which are determined by the discretization for solving the stochastic differential equation (SDE, for short) in forward-backward stochastic differential equations (FBSDEs, for short), which is on the basis of Itô Taylor expansion, the numerical SDE theory, and numerical FBSDEs theory. Under the weak convergence analysis of FBSDEs, we further establish better error estimates of recent numerical schemes for solving FBSDEs.

In this paper, a two-player nonzero-sum stochastic differential game problem is studied with both players using switching controls. A verification theorem associated with a set of variational inequalities is established as a sufficient criterion for Nash equilibrium, in which the equilibrium switching strategies for the two players, indicating when and where it is optimal to switch, are characterized in terms of the so-called switching regions and continuation regions. The verification theorem is proved in a piecewise way along the sequence of total decision times of the two players. Then, some detailed explanations are also provided to illustrate the idea why the conditions are imposed in the verification theorem.

In this paper, we firstly introduce the definition of the fuzzy metric of sets, and discuss the properties of fuzzy metric induced by the Hausdorff metric. Then we prove the limit theorems for set-valued random variables in fuzzy metric space; the convergence is about fuzzy metric induced by the Hausdorff metric. The work is an extension from the classical results for set-valued random variables to fuzzy metric space.