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Representations of hermite processes using local time of intersecting stationary stable regenerative sets

Part of: Stochastic processes

Published online by Cambridge University Press:  23 November 2020

Shuyang Bai
Shuyang Bai*
Affiliation:
University of Georgia, US
*
*Postal address: Department of Statistics, University of Georgia, 310 Herty Drive, Athens, GA 30602, USA. Email address: bsy9142@uga.edu
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Abstract

Hermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

Keywords

Hermite processmultiple Wiener–Itô integralstable regenerative setlocal timelong-range dependencerandom interval covering

MSC classification

Primary: 60G18: Self-similar processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1234 - 1251
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Copyright
© Applied Probability Trust 2020

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