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Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  25 February 2021

Denis Denisov Open the ORCID record for Denis Denisov [Opens in a new window] ,
Elena Perfilev  and
Vitali Wachtel
Denis Denisov*
Affiliation:
University of Manchester
Elena Perfilev*
Affiliation:
Universität Augsburg
Vitali Wachtel*
Affiliation:
Universität Augsburg
*
*Postal address: Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK. Email address: denis.denisov@manchester.ac.uk
**Postal address: Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany.
**Postal address: Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany.
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Abstract

We study the tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asymptotics for tail probabilities for the area.

Keywords

Random walksubexponential distributionheavy-tailed distributionintegrated random walk

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60F17: Functional limit theorems; invariance principles
Type
Research Papers
Information
Journal of Applied Probability , Volume 58 , Issue 1 , March 2021 , pp. 217 - 237
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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