Research On The Truncated Euler-maruyama Methods Of Stochastic Differential Delay Equation

The application of stochastic delay differential equations(SDDE)has been very extensive.Since it is difficult to obtain ture solutions,numerical solutions become the focus of people's research.Therefore,it is difficult and important to construct a numerical solution with strong convergence.in the 2015 year,Mao X proposed the truncated EM method for numerical solution of stochastic differential equation.On this basis,Guo Q has studied the nonlinear SDDE's truncated EM method.Therefore,in this paper,under the local Lipschitz condition and generalized linear growth condition,we mainly research the strong convergence of the truncated EM solution,At the same time,we can get stronger convergence by adding conditions.Secondly,the convergence rate of the truncated EM solution in time T is obtained,Finally,the truncated EM method of stochastic differential equation with variable delays and its convergence are investigated.In this paper,we make full use of the properties of stochastic integrals,and the properties of inequalities prove that under the local Lipschitz condition,generalized linear growth condition and other additional conditions,the strong convergence of the truncated EM solution,and the convergence rate of the truncated EM solution in time T can be gained.Moreover,we investigated the truncated EM method of stochastic differential equation with variable delays and its strong convergence.