Electronic Journal of Probability

A Local Limit Theorem for sums of independent random vectors

Dmitry Dolgopyat

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Abstract

We prove a local limit theorem for sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bounded.

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 39, 15 pp.

Dates
Received: 11 April 2015
Accepted: 17 May 2016
First available in Project Euclid: 15 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465991837

Digital Object Identifier
doi:10.1214/16-EJP4232

Mathematical Reviews number (MathSciNet)
MR3515569

Zentralblatt MATH identifier
1345.60014

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

Keywords
local limit theorem characteristic function lattice distribution concentration inequality

Rights
Creative Commons Attribution 4.0 International License.

Citation

Dolgopyat, Dmitry. A Local Limit Theorem for sums of independent random vectors. Electron. J. Probab. 21 (2016), paper no. 39, 15 pp. doi:10.1214/16-EJP4232. https://projecteuclid.org/euclid.ejp/1465991837


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References

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Electronic Journal of Probability

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