Semi-heavy tails

Edward Omey; Stefan Van Gulck; Rein Vesilo

doi:10.1007/s10986-018-9417-0

Semi-heavy tails

Edward Omey^*, Stefan Van Gulck, Rein Vesilo

^*Corresponding author for this work

School of Engineering

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

7 Citations (Scopus)

Abstract

In this paper, we study properties of functions and sequences with a semi-heavy tail, that is, functions and sequences of the form w(x) = e^−βxf(x), β > 0, resp., w_n = cⁿf_n, 0 < c < 1, where the function f(x), resp., the sequence (f_n), is regularly varying. Among others, we give a representation theorem and study convolution properties. The paper includes several examples and applications in probability theory.

Original language	English
Pages (from-to)	480-499
Number of pages	20
Journal	Lithuanian Mathematical Journal
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/s10986-018-9417-0
Publication status	Published - Oct 2018

Keywords

semi-heavy tail
regular variation
convolutions
asymptotic behaviour
subordination
DISTRIBUTIONS
26A12
33B99
60K05

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10.1007/s10986-018-9417-0

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abstract = "In this paper, we study properties of functions and sequences with a semi-heavy tail, that is, functions and sequences of the form w(x) = e−βxf(x), β > 0, resp., wn = cnfn, 0 < c < 1, where the function f(x), resp., the sequence (fn), is regularly varying. Among others, we give a representation theorem and study convolution properties. The paper includes several examples and applications in probability theory.",

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author = "Edward Omey and {Van Gulck}, Stefan and Rein Vesilo",

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AU - Van Gulck, Stefan

AU - Vesilo, Rein

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N2 - In this paper, we study properties of functions and sequences with a semi-heavy tail, that is, functions and sequences of the form w(x) = e−βxf(x), β > 0, resp., wn = cnfn, 0 < c < 1, where the function f(x), resp., the sequence (fn), is regularly varying. Among others, we give a representation theorem and study convolution properties. The paper includes several examples and applications in probability theory.

AB - In this paper, we study properties of functions and sequences with a semi-heavy tail, that is, functions and sequences of the form w(x) = e−βxf(x), β > 0, resp., wn = cnfn, 0 < c < 1, where the function f(x), resp., the sequence (fn), is regularly varying. Among others, we give a representation theorem and study convolution properties. The paper includes several examples and applications in probability theory.

KW - semi-heavy tail

KW - regular variation

KW - convolutions

KW - asymptotic behaviour

KW - subordination

KW - DISTRIBUTIONS

KW - 26A12

KW - 33B99

KW - 60K05

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EP - 499

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

IS - 4

ER -

Semi-heavy tails

Abstract

Keywords

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