文章基本信息

标题：Parameter Estimation of Complex Fractional Ornstein-Uhlenbeck Processes with Fractional Noise
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作者：Yong Chen ; Yaozhong Hu ; Zhi Wang 等
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：613-629
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We obtain strong consistency and asymptotic normality of a leastsquares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeckprocesses disturbed by fractional noise, extending the result of Hu and Nualart(2010) to a special 2-dimensions. The strategy is to exploit the Garsia-Rodemich-Rumsey inequality and complex fourth moment theorems. The main ingredients ofthis paper are the sample path regularity of a multiple Wiener-Itˆo integral and twoequivalent conditions of complex fourth moment theorems in terms of the contractionsof integral kernels and complex Malliavin derivatives.
关键词：Complex Wiener-Itˆo multiple integral; fractional Brownian motion;fractional Ornstein-Uhlenbeck process; fourth moment theorems; strong consistency; asymptotic;normality.