The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise

Gerardo Barrera; Michael A. Högele; Juan Carlos  Pardo

doi:10.1214/21-EJP685

The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise

Gerardo Barrera, Michael A. Högele, Juan Carlos Pardo

Department of Mathematics and Statistics

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

This paper provides an extended case study of the cutoff phenomenon for a prototypical class of nonlinear Langevin systems with a single stable state perturbed by an additive pure jump Lévy noise of small amplitude, where the driving noise process is of layered stable type.

Original language	English
Article number	119
Journal	Electronic Journal of Probability
Volume	26
Pages (from-to)	1-76
Number of pages	76
ISSN	1083-6489
DOIs	https://doi.org/10.1214/21-EJP685
Publication status	Published - 2021
MoE publication type	A1 Journal article-refereed

Fields of Science

112 Statistics and probability
Cutoff phenomenon
Abrupt thermalization
Exponential ergodicity
Stable Lévy processes
Local limit theorem
Nonlinear coupling
Short coupling
Total variation distance

Access to Document

10.1214/21-EJP685Licence: CC BY

21-EJP685Licence: CC BY

Cite this

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title = "The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise",

abstract = "This paper provides an extended case study of the cutoff phenomenon for a prototypical class of nonlinear Langevin systems with a single stable state perturbed by an additive pure jump L{\'e}vy noise of small amplitude, where the driving noise process is of layered stable type.",

keywords = "112 Statistics and probability, Cutoff phenomenon, Abrupt thermalization, Exponential ergodicity, Stable L{\'e}vy processes, Local limit theorem, Nonlinear coupling, Short coupling, Total variation distance",

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year = "2021",

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journal = "Electronic Journal of Probability",

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publisher = "University of Washington, Mathematics Department",

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AU - Barrera, Gerardo

AU - Högele, Michael A.

AU - Pardo, Juan Carlos

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AB - This paper provides an extended case study of the cutoff phenomenon for a prototypical class of nonlinear Langevin systems with a single stable state perturbed by an additive pure jump Lévy noise of small amplitude, where the driving noise process is of layered stable type.

KW - 112 Statistics and probability

KW - Cutoff phenomenon

KW - Abrupt thermalization

KW - Exponential ergodicity

KW - Stable Lévy processes

KW - Local limit theorem

KW - Nonlinear coupling

KW - Short coupling

KW - Total variation distance

U2 - 10.1214/21-EJP685

DO - 10.1214/21-EJP685

M3 - Article

VL - 26

SP - 1

EP - 76

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

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