The Asymptotic Problem Of The Bayes Estimates For Some Stochastic Differential Equations With Multiscales

Stochastic differential equations are widely used in many fields,such as stochastic con-trol and mathematical fnance.In this paper,we mainly consider stochastic differential equa-tions with perturbations,study the Bayesian estimation of their parameters,and discuss the asympto tic properties of Bayesian estimators under small perturbations.Firstly,the likelihood function of stochastic differential equation with perturbation term is obtained by Girsanov theoem,and the Bayesian estimation of parameters under quadrat-ic loss function is obtained,the small perturbation term ten ds to zero and time T tends to infinity,the Bayesian estimators with unknown parameters is asymptotic normality,and the small perturbation term tends to zero,the parameter estimators had asymptotic consistentcy.Secondly,we improve the model of Chapter 3 to obtain more complex stochastic differential equations,and the unknown parameters is estimated,the effects of the small perturbation ter-m and the time T on the asymptotic properties of Bayesian estimators are discussed.Finally,a two-dimensional stochastic differential equation driven by fractional Brownian motion is introduced,using the stochastic integral theory of fractional Brownian motion and Girsanov theorem,we obtain the Bayesian estimators of parameters,the asymptotic normality and asymptotic consistency of the Bayesian estimators are discussed when the small perturba-tion term tends to zero or the time T tends to infinity,respectively.