论文标题
Malliavin微积分技术用于局部渐近混合正态性及其在退化扩散的应用
Malliavin calculus techniques for local asymptotic mixed normality and their application to degenerate diffusions
论文作者
论文摘要
我们研究了统计模型的局部渐近混合正态性能的足够条件。我们开发了一个计划，其中$ l^2 $规律性条件由Jeganathan [\ textit {sankhya ser。 a} \ textbf {44}（1982）173--212]，使其适用于随机过程的高频观察。此外，通过与gobet [\ textIt {bernoulli} \ textbf {7}（2001）899--912，2001]结合使用malliavin conculus技术，我们引入了足够的条件，以使Mallonson-andition-type估算的Malliavin Sense中平稳遵守。与文献中不同的结果，即使过渡密度函数具有零，也可以应用。对于应用，我们显示了在完整和部分观察框架中，在高频观测下，在高频观测下归化（低纤维化）扩散模型的局部渐近混合正态性。前者和后者分别扩展了椭圆扩散和整合扩散的先前结果。
We study sufficient conditions for a local asymptotic mixed normality property of statistical models. We develop a scheme with the $L^2$ regularity condition proposed by Jeganathan [\textit{Sankhya Ser. A} \textbf{44} (1982) 173--212] so that it is applicable to high-frequency observations of stochastic processes. Moreover, by combining with Malliavin calculus techniques by Gobet [\textit{Bernoulli} \textbf{7} (2001) 899--912, 2001], we introduce tractable sufficient conditions for smooth observations in the Malliavin sense, which do not require Aronson-type estimates of the transition density function. Our results, unlike those in the literature, can be applied even when the transition density function has zeros. For an application, we show the local asymptotic mixed normality property of degenerate (hypoelliptic) diffusion models under high-frequency observations, in both complete and partial observation frameworks. The former and the latter extend previous results for elliptic diffusions and for integrated diffusions, respectively.
