Asymptotic Behaviour of the Trajectory Fitting Estimator for Reflected Ornstein–Uhlenbeck Processes

The Ornstein–Uhlenbeck process with reflection, which has been the subject of an enormous body of literature, both theoretical and applied, is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. In this work, we are mainly concer...

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Bibliographic Details
Published inJournal of theoretical probability Vol. 32; no. 1; pp. 183 - 201
Main Authors Zang, Qingpei, Zhang, Lixin
Format Journal Article
LanguageEnglish
Published New York Springer US 15.03.2019
Springer Nature B.V
Subjects
Asymptotic properties
Consistency
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
Trajectory analysis
Secondary 62F12
Trajectory fitting estimator
Primary 60F15
Reflected Ornstein–Uhlenbeck processes
Nonergodic
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Summary:The Ornstein–Uhlenbeck process with reflection, which has been the subject of an enormous body of literature, both theoretical and applied, is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. In this work, we are mainly concerned with the study of the asymptotic behavior of the trajectory fitting estimator for nonergodic reflected Ornstein–Uhlenbeck processes, including strong consistency and asymptotic distribution. Moreover, we also prove that this kind of estimator for ergodic reflected Ornstein–Uhlenbeck processes does not possess the property of strong consistency.
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ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-017-0796-7