Does the ratio of Laplace transforms of powers of a function identify the function?

Konstantopoulos, Takis and Yuan, Linglong ORCID: 0000-0002-7851-1631 (2021) Does the ratio of Laplace transforms of powers of a function identify the function? JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 494 (1). p. 124568.

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Official URL: http://dx.doi.org/10.1016/j.jmaa.2020.124568

Abstract

We study the following question: if $f$ is a nonzero measurable function on $[0,\infty)$ and $m$ and $n$ distinct nonnegative integers, does the ratio $\widehat{f^n}/\widehat{f^m}$ of the Laplace transforms of the powers $f^n$ and $f^m$ of $f$ uniquely determine $f$? The answer is yes if one of $m, n$ is zero, by the inverse Laplace transform. Under some assumptions on the smoothness of $f$ we show that the answer in the general case is also affirmative. The question arose from a problem in economics, specifically in auction theory where $f$ is the cumulative distribution function of a certain random variable. This is also discussed in the paper.

Item Type:	Article
Uncontrolled Keywords:	Laplace transform, Order statistics, Auction theory
Depositing User:	Symplectic Admin
Date Deposited:	21 Sep 2020 10:02
Last Modified:	09 Feb 2023 04:59
DOI:	10.1016/j.jmaa.2020.124568
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3101583