In this paper, the improved split-step ? method, named composite is proposed to study mean-square stability for stochastic differential equations with a fixed time delay. Under global Lipschitz and linear growth conditions, it proved that method ??0.5 shows stability. An approach improving numerical illustrated by choices of parameters method. Some examples are presented show accordance between...

In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing new adjoint equation, establish sufficient verification theorem for optimal strategies leader and follower in general case. Then, focus on linear–quadratic (LQ) with delay. The equilibrium is presented generalized fully coup...

Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach b...