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February 2018 Abrupt convergence for a family of Ornstein–Uhlenbeck processes
Gerardo Barrera
Braz. J. Probab. Stat. 32(1): 188-199 (February 2018). DOI: 10.1214/16-BJPS337

Abstract

We consider a family of Ornstein–Uhlenbeck processes. Under some suitable assumptions on the behaviour of the drift and diffusion coefficients, we prove profile cut-off phenomenon with respect to the total variation distance in the sense of the definition given by Barrera and Ycart [ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 445–458]. We compute explicitly the cut-off time, the window time, and the profile function. Moreover, we prove that the average process satisfies a profile cut-off phenomenon with respect to the total variation distance. Also, a sample of $N$ Ornstein–Uhlenbeck processes has a window cut-off with respect to the total variation distance in the sense of the definition given by Barrera and Ycart [ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 445–458]. The cut-off time and the cut-off window for the average process and for the sampling process are the same.

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Gerardo Barrera. "Abrupt convergence for a family of Ornstein–Uhlenbeck processes." Braz. J. Probab. Stat. 32 (1) 188 - 199, February 2018. https://doi.org/10.1214/16-BJPS337

Information

Received: 1 December 2015; Accepted: 1 September 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06973954
MathSciNet: MR3770869
Digital Object Identifier: 10.1214/16-BJPS337

Keywords: cut-off phenomenon , Ornstein–Uhlenbeck processes , total variation distance

Rights: Copyright © 2018 Brazilian Statistical Association

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Vol.32 • No. 1 • February 2018
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