On the functional and local limit theorems for Markov modulated compound Poisson processes

Guodong Pang, Yi Zheng

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study a class of Markov-modulated compound Poisson processes whose arrival rates and the compound random variables are both modulated by a stationary finite-state Markov process. The compound random variables are i.i.d. in each state of the Markov process, while having a distribution depending on the state of the Markov process. We prove a functional central limit theorem and local limit theorems under appropriate scalings of the arrival process, compound random variables and underlying Markov process.

Original languageEnglish (US)
Pages (from-to)131-140
Number of pages10
JournalStatistics and Probability Letters
Volume129
DOIs
StatePublished - Oct 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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