Distribution of the maximum and decay rates for renewal processes with application to Hawkes processes
Speaker: Luis Ivan Hernandez Ruiz
Affiliation: Kyoto University
Abstract
In this work we study the distribution of the maximum value for a process that evolves between the epochs of a renewal process under the assumption of the regenerative property and apply the results to the intensity process and the backward recurrence time of a renewal point process. Additionally, we use a coupling argument to find power decay rates for the Key Renewal Theorem in the spread out case and use the result to prove a law of large numbers for a renewal Hawkes process.
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