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

Qingpei Zang () and Lixin Zhang
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Qingpei Zang: Huaiyin Normal University
Lixin Zhang: Zhejiang University

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 183-201

Abstract: Abstract 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.

Keywords: Reflected Ornstein–Uhlenbeck processes; Trajectory fitting estimator; Nonergodic; Primary 60F15; Secondary 62F12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-017-0796-7

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