TY - JOUR
T1 - On the functional and local limit theorems for Markov modulated compound Poisson processes
AU - Pang, Guodong
AU - Zheng, Yi
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/10
Y1 - 2017/10
N2 - 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.
AB - 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.
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U2 - 10.1016/j.spl.2017.05.009
DO - 10.1016/j.spl.2017.05.009
M3 - Article
AN - SCOPUS:85020412251
SN - 0167-7152
VL - 129
SP - 131
EP - 140
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -