STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES

1.进一步研究了具有跳跃/非跳跃判别滤波的M-估计，并给出了该估计的渐近性质。研究了一类连续观测扩散过程的变点问题，得到了渐近性质。该估计器由一个具有良好性质的初始估值器构造，避免了信息的退化问题。引入了一个新的大偏差不等式，研究了M-估计和Bayesian型估计的渐近性质。将所得结果应用于扩散过程的估计，得到了几个新的结果。给出了统计随机场的统一估计。所讨论的统计随机场实质上是无界参数空间上的随机场，而大偏差估计通过连接全局估计和局部渐近二次结构对程序的实现起着至关重要的作用。研究了带跳跃的随机微分方程的Euler-Maruyama逼近的误差界。

1. An M-estimator with jump/non-jump discrimination filter was further investigated and the asymptotic behavior of the estimator was derived.2. The change point problem for a continuously observed diffusion process was studied and the asymptotic properties were found. The estimator was constructed by an initial estimator that possesses a nice property, to avoid the degeneracy problem of the information.3. A new large deviation inequality was introduced and the asymptotic properties of the M-estimator and the Bayesian type estimators were investigated. The result was applied to estimation for a diffusion process and several new results were obtained. A uniform estimate for the statistical random field was provided. The statistical random field in question essentially becomes a random field over a non-bounded parameter space, and an large deviation estimate plays an essential role to realize the program by connecting a global estimate and the loeal asymptotic quadratic structure.4. The error bound of the Euler-Maruyama approximation for the stochastic differential equation with jumps was studied.