Asymptotic statistical Inference theory for stochastic process

随机过程的渐近统计推断理论

基本信息

批准号：
11680319
负责人：
YOSHIDA Nakahiro
金额：
$ 2.24万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

1. We presented an asymptotic expansion to a continuous-time Markov process satisfying the mixing condition. The conditional type Cramer condition in discrete-time setting was replaced by the nondegeneracy condition of the Malliavin covariance of the functional. This method applied to stochastic differential equations. The validity problem was at the same time solved.2. Result 1 was applied to statistical parametric models, and expansions for M-estimators were derived. For diffusion models, this paper completely described the coefficients in the formulae. This, together with Result 1 and Result 5 below, has been the fundamental literature in this field, and it is applied to various statistical problems today.3. For statistical models of diffusion processes with small noises, we derived so-called information criteria for model selection.4. When the security price is described by a general nonlinear stochastic differential equation, it is a difficult problem to compute the value of a der … More ivative. However, it is possible to approximate it by means of the asymptotic expansion technique. This method was introduced by the author and recently many authors pursuit this method. Result 4 treated a practical situation, that is, the equation of the security has unknown parameters. This paper assessed the effects of substitution of estimators to the approximation of option prices, and proposed a correct way to the good approximation.5. Since for a stochastic differential equation with random coefficients of long memory, the usual mixing condition was brokenn, a new methodology is necessary to derive asymptotic expansions. Result 5 introduced the notion of partial mixing and successfully derived asymptotic expansions (of course with validity). Moreover, it showed a practical convenient method with the support theorem to verify the local nondegeneracy of the Malliavin covariance of the expanded functional. This new device enables us to derive expansions very easily, like i.i.d. models.6. Conditional expectation is a most irregular functional in limit theorems. We applied the Malliavin calculus to derive asymptotic expansion of the conditional expectation. This result was applied to the stochastic differential equation with jumps and filtering problems. Less

1。我们提出了满足混合条件的连续时间马尔可夫工艺的不对称扩展。离散时间设置中的条件类型CRAMER条件被功能的Malliavin协方差的非排定条件所取代。该方法应用于随机微分方程。有效性问题同时解决了2。结果1应用于统计参数模型，并得出了M估计器的扩展。对于扩散模型，本文完全描述了公式中的核心。这是结果1和下面的结果5，是该领域的基本文献，它适用于今天的各种统计问题。3。对于具有小声音的差异过程的统计模型，我们得出了用于模型选择的所谓信息标准。4。当安全价格由一般的非线性随机微分方程描述时，很难计算der的价值……更具态度。但是，可以通过不对称扩展技术近似它。该方法是由作者引入的，最近许多作者追求这种方法。结果4处理了实际情况，即安全性方程的参数未知。本文评估了估计量对期权价格近似的影响，并提出了正确近似值的正确方法。5。由于对于具有长期记忆的随机兼容性的随机微分方程，通常会破坏了通常的混合条件，因此需要一种新方法来推导不对称的扩展。结果5引入了部分混合的通知和成功得出的不对称扩展（当然具有有效性）。此外，它显示了一种实用的方便方法，并具有支持定理，以验证扩展功能的Malliavin协方差的局部非排定。这个新设备使我们能够像I.I.D.一样轻松地得出扩展。模型6。条件期望在极限定理中是最不规则的功能。我们应用了Malliavin计算来得出条件期望的渐近扩展。将此结果应用于随机微分方程，并带有跳跃和过滤问题。较少的