Mean Square Stability Of Solutions For Stochastic Discrete Economic Models

In recent years,Stochastic differential equations(SDES)have developed rapidly and attracted the attention of experts and scholars in many fields.In this paper,two kinds of stochastic economic models are constructed.By using Euler-Maruyama method,Lyapunov function and discrete Ito formula,the asymptotic mean square stability of the models solution are studied.The first chapter is the introduction of this paper.It mainly introduces the research background and significance of this paper,as well as the research status of stochastic differential equations and stochastic delay differential equations.The second chapter mainly introduces the theoretical knowledge needed in this paper.In Chapter 3,we mainly study a stochastic discrete model of advertising volume-shopping level.After linearizing the model,we construct Lyapunov function to obtain the sufficient condition for the asymptotic stability of the linear model at zero and the sufficient condition for the asymptotic stability of the stochastic model at positive equilibrium.The final result is verified by numerical simulation.In Chapter 4,we mainly study a class of stochastic discrete model with time delay on corporate cooperative competition.Firstly,we linearize the model at the positive equilibrium point,deal with the delay variable through related inequality,construct a suitable Lyapunov function,and obtain a sufficient condition for the asymptotic mean square stability of the linear model at the zero point,that is,the positive equilibrium of the stochastic discrete model with time delay.The fifth chapter summarizes the paper,reflects on the shortcomings,and makes prospects for future research.