{"product_id":"long-range-dependence-of-markov-chains-von-kristine-joy-carpio","title":"Long-Range Dependence of Markov Chains","description":"\u003cp\u003eLong-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).\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783843394956\"\u003e\u003ch3\u003eTheory and Examples\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783843394956","offer_id":39486433230941,"sku":"9783843394956","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/c2a79287-9d05-41fd-a213-b7b9cef44d2a.jpg?v=1773298485","url":"https:\/\/shop.autorenwelt.de\/en\/products\/long-range-dependence-of-markov-chains-von-kristine-joy-carpio","provider":"Autorenwelt Shop","version":"1.0","type":"link"}