Apr 2022 - Mar 2023

Math-Fi seminar on 20 Oct.

2022.10.18 Tue up
  • Date: 20 Oct. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Luis Iván Hernández Ruíz (Kyoto University)
  • Title: Results on Limit Theorems for the Renewal Hawkes Process
  • Abstract:
Point processes are often used to model occurrences of events in time. One of such models that has seen applications in Finance is the self-exciting process proposed by Hawkes in 1971, in which previous occurrences of events increase the chance for new events to occur.  In this process, immigrants arrive to the system following a Poisson process, then, each immigrant has the possibility to have offspring. At the same time, each new offspring individual has the possibility to give birth to further offspring. In this work, we present an extension to the original Hawkes process, but we consider that the arrival of immigrants is given by a Renewal process; the interarrival times are still independent, but they follow an arbitrary distribution. Existence is proved by exploiting the cluster structure of the process and we use martingale theory to prove a Law of Large Numbers. We give a conjecture for a functional Central Limit Theorem.

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