Coefficients of ergodicity for stochastically monotone Markov chains
In this paper we show that to each distance d defined on the finite state space S of a strongly ergodic Markov chain there corresponds a coefficient ρ d of ergodicity based on the Wasserstein metric. For a class of stochastically monotone transition matrices P , the infimum over all such coefficient...
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| Veröffentlicht in: | Journal of applied probability 1992-12, Vol.29 (4), p.850-860 |
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| container_title | Journal of applied probability |
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| creator | Pflug, G. Ch Schachermayer, W. |
| description | In this paper we show that to each distance
d
defined on the finite state space
S
of a strongly ergodic Markov chain there corresponds a coefficient
ρ
d
of ergodicity based on the Wasserstein metric. For a class of stochastically monotone transition matrices
P
, the infimum over all such coefficients is given by the spectral radius of
P – R
, where
R
= lim
k
P
k
and is attained. This result has a probabilistic interpretation of a control of the speed of convergence of
by the metric
d
and is linked to the second eigenvalue of
P. |
| doi_str_mv | 10.1017/S0021900200043722 |
| format | Article |
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d
defined on the finite state space
S
of a strongly ergodic Markov chain there corresponds a coefficient
ρ
d
of ergodicity based on the Wasserstein metric. For a class of stochastically monotone transition matrices
P
, the infimum over all such coefficients is given by the spectral radius of
P – R
, where
R
= lim
k
P
k
and is attained. This result has a probabilistic interpretation of a control of the speed of convergence of
by the metric
d
and is linked to the second eigenvalue of
P.</description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.1017/S0021900200043722</identifier><language>eng</language><ispartof>Journal of applied probability, 1992-12, Vol.29 (4), p.850-860</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c902-4ee88c15472ff084aa773164a299f304ae212c4423f2c2895e4b97e42a340a493</citedby><cites>FETCH-LOGICAL-c902-4ee88c15472ff084aa773164a299f304ae212c4423f2c2895e4b97e42a340a493</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Pflug, G. Ch</creatorcontrib><creatorcontrib>Schachermayer, W.</creatorcontrib><title>Coefficients of ergodicity for stochastically monotone Markov chains</title><title>Journal of applied probability</title><description>In this paper we show that to each distance
d
defined on the finite state space
S
of a strongly ergodic Markov chain there corresponds a coefficient
ρ
d
of ergodicity based on the Wasserstein metric. For a class of stochastically monotone transition matrices
P
, the infimum over all such coefficients is given by the spectral radius of
P – R
, where
R
= lim
k
P
k
and is attained. This result has a probabilistic interpretation of a control of the speed of convergence of
by the metric
d
and is linked to the second eigenvalue of
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d
defined on the finite state space
S
of a strongly ergodic Markov chain there corresponds a coefficient
ρ
d
of ergodicity based on the Wasserstein metric. For a class of stochastically monotone transition matrices
P
, the infimum over all such coefficients is given by the spectral radius of
P – R
, where
R
= lim
k
P
k
and is attained. This result has a probabilistic interpretation of a control of the speed of convergence of
by the metric
d
and is linked to the second eigenvalue of
P.</abstract><doi>10.1017/S0021900200043722</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9002 |
| ispartof | Journal of applied probability, 1992-12, Vol.29 (4), p.850-860 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_crossref_primary_10_1017_S0021900200043722 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| title | Coefficients of ergodicity for stochastically monotone Markov chains |
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