Statistical aspects of the fractional stochastic calculus

• 成果类型: Article
• 署名作者: Tudor, Ciprian A.; Viens, Frederi G.
• 署名单位: heSam Universite; Universite Pantheon-Sorbonne; Purdue University System; Purdue University; Purdue University System; Purdue University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001541
• 发表日期: 2007
• 页码: 1183-1212
• 关键词: maximum-likelihood-estimation; differential-equations; inference; models

摘要

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by a fractional Brownian motion with arty level of Holder-regularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We also prove that a version of the MLE using only discrete observations is still a strongly consistent estimator.