Parametric inference for discretely observed non-ergodic diffusions
Parametric inference for discretely observed non-ergodic diffusions
复制标题
离散观察的非遍历扩散的参数推断
DOI：
10.3150/bj/1151525127
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发表时间：
2006
期刊：
影响因子：
1.5
通讯作者：
J. Jacod
中科院分区：
文献类型：
--
作者：
J. Jacod
考虑一个多维扩散过程X，其漂移系数和扩散系数分别依赖于参数A和0。这个过程是在n 41个等间隔的时间0，A？，2A？，..., ? A？所以Tn =？一个？表示“观察窗口”的长度。我们感兴趣的是估计A和/或6。在适当的光滑性和可识别性条件下，我们给出了估计量Xn和0？，使得变量y/n~（6 n 0）和y/T^（Xn A）对A是紧的？? 0和Tn？* oo.当A是已知的，我们甚至可以放弃假设T？? oo.这些结果在没有对扩散过程作任何遍历性或递归性假设的情况下仍然成立。
We consider a multidimensional diffusion process X whose drift and diffusion coefficients depend respectively on a parameter A and 0. This process is observed at n 41 equally spaced times 0, A?, 2A?, ..., ?A?, and Tn = ?A? denotes the length of the 'observation window'. We are interested in estimating A and/or 6. Under suitable smoothness and identifiability conditions, we exhibit estimators Xn and 0?, such that the variables y/n~(6n 0) and y/T^(Xn A) are tight for A? ? 0 and Tn ?* oo. When A is known, we can even drop the assumption that T? ? oo. These results hold without any kind of ergodicity or even recurrence assumption on the diffusion process.