Parameter estimation based on discrete observations of fractional Ornstein–Uhlenbeck process of the second kind

被引：3
|
作者：
Azmoodeh E. [1 ]
Viitasaari L. [2 ]
机构：
[1] Mathematics Research Unit, Luxembourg University, P.O. Box L-1359, Luxembourg-Kirchberg
[2] Department of Mathematics and System Analysis, Aalto University School of Science, Helsinki, P.O. Box 11100, Aalto
来源：
Statistical Inference for Stochastic Processes | 2015年 / 18卷 / 3期
关键词：
Central limit theorem (CLT); Fractional Ornstein–Uhlenbeck processes; Malliavin calculus; Multiple Wiener integrals; Parameter estimation;
D O I：
10.1007/s11203-014-9111-8
中图分类号：
学科分类号：
摘要：
Fractional Ornstein–Uhlenbeck process of the second kind (fOU2) is a solution of the Langevin equation (Formula presented.) with a Gaussian driving noise (Formula presented.), where (Formula presented.) and B is a fractional Brownian motion with Hurst parameter H∈(0,1). In this article we consider the case H>12, and by using the ergodicity of fOU2 process we construct consistent estimators for the drift parameter θ based on discrete observations in two possible cases:(i) the Hurst parameter H is known and (ii) the Hurst parameter H is unknown. Moreover, using Malliavin calculus techniques we prove central limit theorems for our estimators which are valid for the whole range H∈(12,1). © 2014, Springer Science+Business Media Dordrecht.
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页码：205 / 227
页数：22
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