Large deviations for product of sums of random variables

Lingjiong Zhu

doi:10.1016/j.spl.2014.02.012

Large deviations for product of sums of random variables

Lingjiong Zhu

School of Mathematics

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

1 Scopus citations

Abstract

In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed.

Original language	English (US)
Pages (from-to)	17-22
Number of pages	6
Journal	Statistics and Probability Letters
Volume	89
Issue number	1
DOIs	https://doi.org/10.1016/j.spl.2014.02.012
State	Published - Jun 2014

Bibliographical note

Funding Information:
The author thanks an anonymous referee for the helpful suggestions. The author is supported by NSF Grant DMS-0904701 , DARPA Grant and MacCracken Fellowship at New York University .

Keywords

Large deviations
Product of sums of random variables
Sample paths

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10.1016/j.spl.2014.02.012

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abstract = "In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed.",

keywords = "Large deviations, Product of sums of random variables, Sample paths",

author = "Lingjiong Zhu",

note = "Funding Information: The author thanks an anonymous referee for the helpful suggestions. The author is supported by NSF Grant DMS-0904701 , DARPA Grant and MacCracken Fellowship at New York University .",

year = "2014",

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N2 - In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed.

AB - In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed.

KW - Large deviations

KW - Product of sums of random variables

KW - Sample paths

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ER -

Large deviations for product of sums of random variables

Abstract

Bibliographical note

Keywords

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