Regularized distributions and entropic stability of Cramer's characterization of the normal law

S. G. Bobkov; G. P. Chistyakov; F. Götze

doi:10.1016/j.spa.2016.04.010

Regularized distributions and entropic stability of Cramer's characterization of the normal law

S. G. Bobkov, G. P. Chistyakov, F. Götze

School of Mathematics

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

2 Scopus citations

Abstract

For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.

Original language	English (US)
Pages (from-to)	3865-3887
Number of pages	23
Journal	Stochastic Processes and their Applications
Volume	126
Issue number	12
DOIs	https://doi.org/10.1016/j.spa.2016.04.010
State	Published - Dec 1 2016

Bibliographical note

Funding Information:
This research was partially supported by NSF grant DMS-1612961 , the Humboldt Foundation and SFB 701 at Bielefeld University .

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

Cramer's theorem
Normal characterization
Stability problems

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10.1016/j.spa.2016.04.010

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title = "Regularized distributions and entropic stability of Cramer's characterization of the normal law",

abstract = "For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.",

keywords = "Cramer's theorem, Normal characterization, Stability problems",

author = "Bobkov, {S. G.} and Chistyakov, {G. P.} and F. G{\"o}tze",

note = "Funding Information: This research was partially supported by NSF grant DMS-1612961 , the Humboldt Foundation and SFB 701 at Bielefeld University . Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

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AU - Bobkov, S. G.

AU - Chistyakov, G. P.

AU - Götze, F.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.

AB - For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.

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KW - Normal characterization

KW - Stability problems

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Regularized distributions and entropic stability of Cramer's characterization of the normal law

Abstract

Bibliographical note

Keywords

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