Characterization of Convergence Rates for the Approximation of the Stationary Distribution of Infinite Monotone Stochastic Matrices
Identifieur interne : 00C628 ( Main/Merge ); précédent : 00C627; suivant : 00C629Characterization of Convergence Rates for the Approximation of the Stationary Distribution of Infinite Monotone Stochastic Matrices
Auteurs : F. Simonot ; Y.-Q. SongSource :
- Journal of Applied Probability ; 1996.
English descriptors
- KwdEn :
Abstract
Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and Pn be any n x n stochastic matrix with Pn \geq Tn, where Tn denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions \pi and \pi n for P and Pn respectively\, ; we show that if the Markov Chain with transition probability matrix P meets the further condition of geometric recurrence then the exact convergence rate of \pi n to \pi can be expressed in term of the radius of convergence of the generating function of \pi. As an application of the preceding result, we deal with the random walk on a half line and prove that the assumption of geometric recurrence can be relaxed, we also show that if the i.i.d input sequence (A(m)) is such that we can find a real number r_0 > 1 with E\left{r_0^A\right} = 1, then the exact convergence rate of \pi n to \pi is characterized by r_{0} Moreover, when the generating function of A is not defined for |z| > 1, we derive an upper bound for the distance between \pi n and \pi based on the moments of A.
Links toward previous steps (curation, corpus...)
- to stream Crin, to step Corpus: 001C35
- to stream Crin, to step Curation: 001C35
- to stream Crin, to step Checkpoint: 002869
Links to Exploration step
CRIN:simonot95cLe document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" wicri:score="967">Characterization of Convergence Rates for the Approximation of the Stationary Distribution of Infinite Monotone Stochastic Matrices</title></titleStmt><publicationStmt><idno type="RBID">CRIN:simonot95c</idno><date when="1996" year="1996">1996</date><idno type="wicri:Area/Crin/Corpus">001C35</idno><idno type="wicri:Area/Crin/Curation">001C35</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Curation">001C35</idno><idno type="wicri:Area/Crin/Checkpoint">002869</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Checkpoint">002869</idno><idno type="wicri:Area/Main/Merge">00C628</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Characterization of Convergence Rates for the Approximation of the Stationary Distribution of Infinite Monotone Stochastic Matrices</title><author><name sortKey="Simonot, F" sort="Simonot, F" uniqKey="Simonot F" first="F." last="Simonot">F. Simonot</name></author><author><name sortKey="Song, Y Q" sort="Song, Y Q" uniqKey="Song Y" first="Y.-Q." last="Song">Y.-Q. Song</name></author></analytic><series><title level="j">Journal of Applied Probability</title><imprint><date when="1996" type="published">1996</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Lindley process</term><term>Markov chain</term><term>convergence rate</term><term>geometric recurrence</term><term>random walk</term><term>skip free condition</term><term>stochastic monotonicity</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en" wicri:score="3960">Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and Pn be any n x n stochastic matrix with Pn \geq Tn, where Tn denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions \pi and \pi n for P and Pn respectively\, ; we show that if the Markov Chain with transition probability matrix P meets the further condition of geometric recurrence then the exact convergence rate of \pi n to \pi can be expressed in term of the radius of convergence of the generating function of \pi. As an application of the preceding result, we deal with the random walk on a half line and prove that the assumption of geometric recurrence can be relaxed, we also show that if the i.i.d input sequence (A(m)) is such that we can find a real number r_0 > 1 with E\left{r_0^A\right} = 1, then the exact convergence rate of \pi n to \pi is characterized by r_{0} Moreover, when the generating function of A is not defined for |z| > 1, we derive an upper bound for the distance between \pi n and \pi based on the moments of A.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Merge
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 00C628 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Merge/biblio.hfd -nk 00C628 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Merge
|type= RBID
|clé= CRIN:simonot95c
|texte= Characterization of Convergence Rates for the Approximation of the Stationary Distribution of Infinite Monotone Stochastic Matrices
}}
| This area was generated with Dilib version V0.6.33. |  |