Long-Range Dependence of Markov Chains Theory and Examples

Name: Long-Range Dependence of Markov Chains
Author: Kristine Joy Carpio

Auteur: Kristine Joy Carpio

Taal: Engels

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Auteur: Kristine Joy Carpio

Uitgever: Lap Lambert Academic Publishing

Engels
Paperback
9783843394956
februari 2011
116 pagina's

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Samenvatting

Long-range dependence in discrete and continuous time Markov chains over a countable state space is defined via embedded renewal processes brought about by visits to a fixed state. In the discrete time chain, solidarity properties are obtained and long-range dependence of functionals are examined. On the other hand, the study of LRD of continuous time chains is defined via the number of visits in a given time interval. Long-range dependence of Markov chains over a non-countable state space is also carried out through positive Harris chains. Examples of these chains are presented, with particular attention given to long-range dependent Markov chains in single-server queues, namely, the waiting times of GI/G/1 queues and queue lengths at departure epochs in M/G/1 queues. The presence of long-range dependence in these processes is dependent on the moment index of the lifetime distribution of the service times. These processes of waiting times and queue sizes are also examined in a range of M/P/2 queues via simulation (here, $P$ denotes a Pareto distribution).

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