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Functional central limit theorems and moderate deviations for Poisson cluster processes
Published online by Cambridge University Press: 24 September 2020
Abstract
In this paper, we consider functional limit theorems for Poisson cluster processes. We first present a maximal inequality for Poisson cluster processes. Then we establish a functional central limit theorem under the second moment and a functional moderate deviation principle under the Cramér condition for Poisson cluster processes. We apply these results to obtain a functional moderate deviation principle for linear Hawkes processes.
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- Original Article
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- © Applied Probability Trust 2020
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