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In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the solutions to the equations by using the method of multiple Lyapunov functions, such as the moment exponential stability, almost sure exponential stability and almost sure polynomial stability, etc.
In this paper, we study the convergence of the Euler-Maruyama numerical solutions for pantograph stochastic functional differential equations which was proposed in [11]. We also show that the numerical solutions have the properties of almost surely p
The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $cR^p$ ($pin [1, infty)$) and backward stochastic differential equations (BSDEs) in $cR^ptimes cH^p$ ($pin (1, infty)$) and in $cR^inftyt
We propose an unbiased Monte-Carlo estimator for $mathbb{E}[g(X_{t_1}, cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen sim
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs for short) have been intensively investigated. In this paper we summarize some recent pro