Parameter Estimation Of Stochastic Differential Equations

In the real world,stochastic phenomenon is ubiquitous because of the in-fluence of noise,so almost all of the system has a certain randomness.Einstein and Wiener who studied the property of Brownian motion before others had given some theoretical results.later,Thanks for Ito defined the stochastic inte-gral and many scholars efforts,stochastic differential equation theory has been improved.Stochastic differential equations is a interdisciplinary sciences com-bined ordinary differential equations,dynamic systems and stochastic analy-sis.And it is extremely important to study financial system model,biological system model and other models.As is known to all,the parameters of the stochastic differential system are unknown in the process of study model.so we analyze the parameters of the model by the existing data,in other words,we estimate the unknown parameters of the overall data through sample data.This is what we call the parameter estimation.Arato,Kolmogorov and Sinai was studied the parameter estimation of the stochastic system in 1962.After that,the research and theory of the parameter estimation stochastic differential equation has made considerable development because of the effort of many scholars.In the first chapter of this paper,the significance of parameter estimation of stochastic differential equations is introduced.And the the important role of stochastic differential equation for finance,statistical physics and other fields is also illuminated,then it comes to a conclusion that the parameter estimation of the stochastic differential equations is extremely important.After that,this chapter presents the development and the outstanding results of the parame-ter estimation of stochastic differential equation.The knowledge of the basic theory of stochastic differential equations is presented in the second chapter.Maximum likelihood estimate method is introduced and new estimation meth-ods will be proposed in the third chapter.In the fourth chapter,Compared the numerical experiments result of maximum likelihood estimation method with the result of the methods proposed in this paper,it shows that the method proposed in this paper is effective.At the same time,we show applications of the method of expectation and variance in this chapter.In the last chapter of this article,we present the full text summary.