Study Of Convergence Of Numerical Methods For Nonlinear Stochastic Differential Equations With Poisson Jump

In the mathematical model that describes the objective law of things,the influence of random factors on the model needs to be considered,and the nonlinear stochastic differential equation with jump can describe this kind of problem more accurately,and is widely used in geophysics,environmental science,economics and artificial neural networks and other fields.Therefore,it is of great significance to study the convergence of numerical solutions of nonlinear stochastic differential equations with jumps.Since the analytical solution of nonlinear stochastic differential equations with hops is difficult to solve,constructing numerical methods to find the approximate solution of equations has important theoretical and practical application value for studying the convergence of numerical solutions of nonlinear stochastic differential equations with hops.In this paper,the convergence of the hybrid Euler method of two types of nonlinear stochastic differential equations with hopping is mainly studied,and the main work is as follows:The first chapter introduces the research background and research status of nonlinear stochastic differential squares with Poisson jump.The second chapter introduces the basics of two types of nonlinear stochastic differential equations with jumps.The third chapter focuses on the convergence of hybrid methods for nonlinear stochastic differential equation with Poisson jumps is studied by constructing hybrid methods.It has been proven that under global conditions,the mixed method is compatible in both the mean and mean square sense,with compatibility orders of 2 and 1,respectively.And it has been proven that the method converges with a convergence order of 1,and corresponding numerical experiments are provided.The experimental results show that the numerical solution and the analytical solution have the same stability properties.The fourth chapter focuses on the convergence of the hybrid Euler method of nonlinear stochastic proportional differential equations with Poisson jump.It is proved that the hybrid Euler method has compatibility and convergence when the global Lipschitz conditions are met,and the convergence order is 0.5.