Limit theorems for a cox-ingersoll-ross process with hawkes jumps

Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll- Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations..

Original languageEnglish (US)
Pages (from-to)699-712
Number of pages14
JournalJournal of Applied Probability
Volume51
Issue number3
DOIs
StatePublished - Sep 1 2014

Keywords

  • Central limit theorem
  • Cox-Ingersoll-Ross process
  • Hawkes process
  • Large deviations
  • Point process
  • Self-exciting process

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