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

Guodong Pang and Yi Zheng

Statistics & Probability Letters, 2017, vol. 129, issue C, 131-140

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.

Keywords: Markov modulated compound Poisson process; Functional central limit theorem; Local limit theorem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2017.05.009

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