KFU. Card publication. Strong power and subexponential laws for an ordered list of trajectories of a Markov chain

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STRONG POWER AND SUBEXPONENTIAL LAWS FOR AN ORDERED LIST OF TRAJECTORIES OF A MARKOV CHAIN

Form of presentation

Articles in international journals and collections

Year of publication

2014

Authors, employees of KFU

Bochkarev Vladimir Vladimirovich, author

Lerner Eduard Yulevich, author

Bibliographic description in the original language

Strong power and subexponential laws for an ordered list of trajectories of a Markov chain. Electronic Journal of Linear Algebra: Vol. 27, Article 252, 2014

Annotation

Consider a homogeneous Markov chain with discrete time and with a finite set of states E0,..., En such that the state E0 is absorbing and states E1,..., En are nonrecurrent. The frequencies of trajectories in this chain are studied in this paper, i.e., words composed of symbols E1,..., En ending with the space E0. Order the words according to their probabilities; denote by p(t) the probability of the t-th word in this list. As was proved recently, in the case of an infinite list of words, in the dependence of the topology of the graph of the Markov chain, there exists either the limit ln p(t)/ ln t as t → ∞ or that of ln p(t)/t^(1/D), where D ∈ N (weak power and subexponential laws). As appeared, in the latter case the decreasing order of the function p(t) is always subexponential (the strong subexponential law). In the first case, this paper describes necessary and sufficient conditions of the power order (the strong power law).

Keywords

Substochastic matrices, Markov chains, directed graphs, strong power laws

The name of the journal

Electronic Journal of Linear Algebra

URL

http://repository.uwyo.edu/cgi/viewcontent.cgi?article=1917&context=ela

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=95310&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bochkarev Vladimir Vladimirovich	ru_RU
dc.contributor.author	Lerner Eduard Yulevich	ru_RU
dc.date.accessioned	2014-01-01T00:00:00Z	ru_RU
dc.date.available	2014-01-01T00:00:00Z	ru_RU
dc.date.issued	2014	ru_RU
dc.identifier.citation	Strong power and subexponential laws for an ordered list of trajectories of a Markov chain. Electronic Journal of Linear Algebra: Vol. 27, Article 252, 2014	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=95310&p_lang=2	ru_RU
dc.description.abstract	Electronic Journal of Linear Algebra	ru_RU
dc.description.abstract	Consider a homogeneous Markov chain with discrete time and with a finite set of states E0,..., En such that the state E0 is absorbing and states E1,..., En are nonrecurrent. The frequencies of trajectories in this chain are studied in this paper, i.e., words composed of symbols E1,..., En ending with the space E0. Order the words according to their probabilities; denote by p(t) the probability of the t-th word in this list. As was proved recently, in the case of an infinite list of words, in the dependence of the topology of the graph of the Markov chain, there exists either the limit ln p(t)/ ln t as t → ∞ or that of ln p(t)/t^(1/D), where D ∈ N (weak power and subexponential laws). As appeared, in the latter case the decreasing order of the function p(t) is always subexponential (the strong subexponential law). In the first case, this paper describes necessary and sufficient conditions of the power order (the strong power law).	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Substochastic matrices	ru_RU
dc.subject	Markov chains	ru_RU
dc.subject	directed graphs	ru_RU
dc.subject	strong power laws	ru_RU
dc.title	Strong power and subexponential laws for an ordered list of trajectories of a Markov chain	ru_RU
dc.type	Articles in international journals and collections	ru_RU