Bayesian Estimation Of Parameters For Some Classes Of Stochastic Differential Equations

Stochastic differential equations(SDEs)are widely used in many fields,such as electronic communication,biology and financial option pricing,etc.Therefore,the problem of parameter estimation of SDEs has attracted much attention from schol-ars.Most studies on parameter estimation so far are based on maximum likelihood method.In practice,however,we often have a certain understanding of the informa-tion of unknown parameters in advance.Consequently,the thesis mainly studies the Bayesian estimators of unknown parameters of stochastic differential equations and their statistical properties.In Chapter 3 we obtain the Bayesian estimation of unknown parameters for a class of stochastic differential equations without perturbed terms.Some statistical proper-ties of Bayesian estimators,such as asymptotic normality,asymptotic consistency and asymptotic unbiasedness,are proved.The properties of the estimator are discussed as time T goes to infinity.Moreover,Chapter 4 contains the Bayesian estimation of unknown parameters for a class of more complex stochastic differential equations with perturbed terms,and,in particular,the expressions of the Bayesian estimators are given.The influence of the small disturbance terms ? on the estimator is discussed and the asymptotic normality,asymptotic consistency and asymptotic unbiasedness of the Bayesian estimator are also proved.Finally,in Chapter 5,the Bayesian estima-tion methods of model parameters in Chapter 3 and Chapter 4 are simulated by using MATLAB software and the performances of simulation results support the theoretical expectations.