Local limit theorems for smoothed bernoulli and other convolutions

S. G. Bobkov; A. Marsiglietti

doi:10.1137/S0040585X97T989829

Local limit theorems for smoothed bernoulli and other convolutions

S. G. Bobkov, A. Marsiglietti

School of Mathematics

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

Abstract

We explore the asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.

Original language	English (US)
Pages (from-to)	62-81
Number of pages	20
Journal	Theory of Probability and its Applications
Volume	65
Issue number	1
DOIs	https://doi.org/10.1137/S0040585X97T989829
State	Published - 2020

Bibliographical note

Funding Information:
∗Received by the editors December 20, 2018. The research of the first author was partially supported by NSF grant DMS-1855575. Originally published in the Russian journal Teoriya Veroy-atnostei i ee Primeneniya, 65 (2020), pp. 79–102. https://doi.org/10.1137/S0040585X97T989829 †School of Mathematics, University of Minnesota, Minneapolis, MN 55455 ([email protected]. edu). ‡Department of Mathematics, University of Florida, Gainesville, FL 32611 (a.marsiglietti@ufl. edu).

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© by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

Central limit theorem
Local limit theorem

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title = "Local limit theorems for smoothed bernoulli and other convolutions",

abstract = "We explore the asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.",

keywords = "Central limit theorem, Local limit theorem",

author = "Bobkov, {S. G.} and A. Marsiglietti",

note = "Funding Information: ∗Received by the editors December 20, 2018. The research of the first author was partially supported by NSF grant DMS-1855575. Originally published in the Russian journal Teoriya Veroy-atnostei i ee Primeneniya, 65 (2020), pp. 79–102. https://doi.org/10.1137/S0040585X97T989829 †School of Mathematics, University of Minnesota, Minneapolis, MN 55455 ([email protected]. edu). ‡Department of Mathematics, University of Florida, Gainesville, FL 32611 (a.marsiglietti@ufl. edu). Publisher Copyright: {\textcopyright} by SIAM. Unauthorized reproduction of this article is prohibited.",

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AU - Marsiglietti, A.

N1 - Funding Information: ∗Received by the editors December 20, 2018. The research of the first author was partially supported by NSF grant DMS-1855575. Originally published in the Russian journal Teoriya Veroy-atnostei i ee Primeneniya, 65 (2020), pp. 79–102. https://doi.org/10.1137/S0040585X97T989829 †School of Mathematics, University of Minnesota, Minneapolis, MN 55455 ([email protected]. edu). ‡Department of Mathematics, University of Florida, Gainesville, FL 32611 (a.marsiglietti@ufl. edu). Publisher Copyright: © by SIAM. Unauthorized reproduction of this article is prohibited.

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AB - We explore the asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.

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Local limit theorems for smoothed bernoulli and other convolutions

Abstract

Bibliographical note

Keywords

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