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2015 Statistical inference for generalized Ornstein-Uhlenbeck processes
Denis Belomestny, Vladimir Panov
Electron. J. Statist. 9(2): 1974-2006 (2015). DOI: 10.1214/15-EJS1063


In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type \[X_{t}=e^{-\xi_{t}}\left(X_{0}+\int_{0}^{t}e^{\xi_{u-}}du \right), \] where $\xi_{s}$ is a Lévy process. Our primal goal is to estimate the characteristics of the Lévy process $\xi$ from the low-frequency observations of the process $X$. We present a novel approach towards estimating the Lévy triplet of $\xi$, which is based on the Mellin transform technique. It is shown that the resulting estimates attain optimal minimax convergence rates. The suggested algorithms are illustrated by numerical simulations.


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Denis Belomestny. Vladimir Panov. "Statistical inference for generalized Ornstein-Uhlenbeck processes." Electron. J. Statist. 9 (2) 1974 - 2006, 2015.


Received: 1 March 2015; Published: 2015
First available in Project Euclid: 31 August 2015

zbMATH: 1337.62230
MathSciNet: MR3393601
Digital Object Identifier: 10.1214/15-EJS1063

Keywords: exponential functional , generalized Ornstein-Uhlenbeck process , Lévy process , Mellin transform

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.9 • No. 2 • 2015
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