Asymptotic Behavior of Rényi Entropy in the Central Limit Theorem

Sergey G. Bobkov; Arnaud Marsiglietti

doi:10.1007/978-3-030-26391-1_11

Asymptotic Behavior of Rényi Entropy in the Central Limit Theorem

Sergey G. Bobkov, Arnaud Marsiglietti

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We explore an asymptotic behavior of Rényi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.

Original language	English (US)
Title of host publication	Progress in Probability
Publisher	Birkhauser
Pages	169-200
Number of pages	32
DOIs	https://doi.org/10.1007/978-3-030-26391-1_11
State	Published - 2019

Publication series

Name	Progress in Probability
Volume	74
ISSN (Print)	1050-6977
ISSN (Electronic)	2297-0428

Bibliographical note

Funding Information:
This research was partially supported by NSF grant DMS-1855575 and BSF grant 2016050. Also, this research was supported in part by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship.

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Central limit theorem
Rényi entropy

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10.1007/978-3-030-26391-1_11

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abstract = "We explore an asymptotic behavior of R{\'e}nyi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.",

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AU - Bobkov, Sergey G.

AU - Marsiglietti, Arnaud

N1 - Funding Information: This research was partially supported by NSF grant DMS-1855575 and BSF grant 2016050. Also, this research was supported in part by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. Publisher Copyright: © 2019, Springer Nature Switzerland AG.

PY - 2019

Y1 - 2019

N2 - We explore an asymptotic behavior of Rényi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.

AB - We explore an asymptotic behavior of Rényi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.

KW - Central limit theorem

KW - Rényi entropy

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DO - 10.1007/978-3-030-26391-1_11

M3 - Chapter

AN - SCOPUS:85118450134

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BT - Progress in Probability

PB - Birkhauser

ER -

Asymptotic Behavior of Rényi Entropy in the Central Limit Theorem

Abstract

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