VARIATIONS AND ESTIMATORS FOR SELF-SIMILARITY PARAMETERS VIA MALLIAVIN 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 PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP459
• 发表日期: 2009
• 页码: 2093-2134
• 关键词: CENTRAL LIMIT-THEOREMS; power variations; CONVERGENCE; functionals

摘要

Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian self-similar process, the Rosenblatt process. We apply our results to the design of strongly consistent statistical estimators for the self-similarity parameter H. Although, in the case of the Rosenblatt process, our estimator has non-Gaussian asymptotics for all H > 1/2, we show the remarkable fact that the process's data at time 1 can be used to construct a distinct, compensated estimator with Gaussian asymptotics for H is an element of (1/2, 2/3).