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Representations of hermite processes using local time of intersecting stationary stable regenerative sets
Published online by Cambridge University Press: 23 November 2020
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.
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- © Applied Probability Trust 2020
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