| 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 ε 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. |
