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

DOI10.1016/J.SPL.2017.05.009zbMath1380.60040OpenAlexW2618446440MaRDI QIDQ1687203

Guodong Pang, Yi Zheng

Publication date: 22 December 2017

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2017.05.009

zbMATH Keywords

functional central limit theoremlocal limit theoremMarkov modulated compound Poisson process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17) Continuous-time Markov processes on discrete state spaces (60J27) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (5)

A multinomial approximation approach for the finite time survival probability under the Markov-modulated risk model ⋮ Diffusion approximation of an infinite-server queue under Markovian environment with rapid switching ⋮ Optimal Control of Markov-Modulated Multiclass Many-Server Queues ⋮ Asymptotics and approximations of ruin probabilities for multivariate risk processes in a Markovian environment ⋮ Exponential ergodicity and steady-state approximations for a class of markov processes under fast regime switching

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A functional central limit theorem for a Markov-modulated infinite-server queue
• Heavy-traffic fluid limits for periodic infinite-server queues
• Local limit theorems for random walks in a 1D random environment
• A local limit theorem for random walks in balanced environments
• Ladder heights and the Markov-modulated M/G/1 queue
• On the ruin problem in a Markov-modulated risk model
• Proofs of the martingale FCLT
• A Markov-modulated M/G/1 queue. I: Stationary distribution
• A Markov-modulated M/G/1 queue. II: Busy period and time for buffer overflow
• A functional central limit theorem for Markov additive arrival processes and its applications to queueing systems
• An elementary proof of the local central limit theorem
• Probability theory. Edited by K. A. Borovkov. Transl. from the Russian by O. Borovkova and P. S. Ruzankin
• An almost sure local limit theorem for Markov chains
• Some results about the expected ruin time in Markov-modulated risk models
• Stochastic-Process Limits
• INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES
• On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue
• The Queue M|G|1 with Markov Modulated Arrivals and Services
• Risk theory in a Markovian environment
• Lundberg parameters for non standard risk processes
• Markov-modulated diffusion risk models
• Large deviations for risk processes with reinsurance

This page was built for publication: On the functional and local limit theorems for Markov modulated compound Poisson processes