Convergence Analysis Of Truncated ? Method For Stochastic Differential Equations

In general,when the convergence of numerical methods of stochastic differential equations is studied,the drift and diffusion terms of the equations are required to satisfy the global Lipschitz condition and the linear growth condition at the same time.However,due to the linear growth condition is too strong,most SDEs models in real life do not obey the linear growth condition.So we construct a new semi-implicit numerical method for the stochastic differnetial equations under the local Lipschitz condition and Khasminskii-type condition,that is,truncated ? method.Meanwhile,we establish the ralated convergence theory.The structure of this paper ia as follows:The first chapter is an introduction.We mainly introduce the background status of stochastic differential equations,the innovation of this paper and the main content.In the second chapter is the preliminary knowledge.We mainly introduce this paper of the basic knowledge and symbols.The third chapter,we construct the implicit truncated ? method.Then,under the local Lipschitz congdition,Khasminskii-type condition and polynomial conditions of diffusion terms,we have successfully shown the strong convergence of both continuous-time truncated ? solutions to the true solution.Finally,the theoretical results are verified by numerical experiments.The fourth chapter,we discuss the convergence rate of the truncated ? method under given conditions.Meanwhile,we show that the order of q-th moment can be arbitrarily close to 1/2.Finally,the theoretical results are verified by numerical experi-ments.Finally,we make a summary and outlook.