Convergence Of Numerical Solutions For Stochastic Differential Equations With Piecewise Continuous Arguments Driven By Poisson Jump

In recent years, as a class of mathematical models, stochastic differential equations with piecewise continuous arguments driven by poisson jump have been widely used to practical problems, especially in astronomy, geography, economics, finance, engineering, signal and other fields. Stochastic differential equations with piecewise continuous arguments driven by poisson jump is a class of models of continuous and discrete dynamical systems, so it can describe the problem objectively. This paper mainly deals with the convergence of numerical solutions for this kind of stochastic system.Firstly, it has been shown that the equation has a unique solution under Non global Lipschitz conditions. Then the tamed Euler method is constructed to apply to stochastic differential equations with piecewise continuous arguments driven by poisson jump, and then the numerical method is proved to be strongly convergent under super linear growth condition.Secondly, we find the key to prove the convergence of numerical method is to prove the pth moments of the numerical solution are bounded on the whole pobability space in the process. So we firstly prove the numerical solution which is obtained the numerical method apply to stochastic differential equations with piecewise continuous arguments driven by poisson jump is pth moments bounded on a subset of pobability space ?. Next, we proof the probability of the complement of this subset is zero.Finally, using the pth moments boundness of numerical solution and the given assumptions, the convergence of numerical method is proved, and the convergence rate is obtained.