Local limit theorems for smoothed bernoulli and other convolutions

S. G. Bobkov, A. Marsiglietti

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
Pages (from-to)62-81
Number of pages20
JournalTheory of Probability and its Applications
Volume65
Issue number1
DOIs
StatePublished - 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 (bobkov@math.umn. 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.

Keywords

  • Central limit theorem
  • Local limit theorem

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