LongRange Dependence of Markov Chains: Theory and Examples,Used

LongRange Dependence of Markov Chains: Theory and Examples,Used

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SKU: DADAX3843394954
Brand: LAP Lambert Academic Publishing
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Longrange 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 longrange 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. Longrange dependence of Markov chains over a noncountable state space is also carried out through positive Harris chains. Examples of these chains are presented, with particular attention given to longrange dependent Markov chains in singleserver queues, namely, the waiting times of GI/G/1 queues and queue lengths at departure epochs in M/G/1 queues. The presence of longrange 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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