InforLorV4, PascalFrancis, Corpus, bibRecord, 000C71

Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices

Identifieur interne : 000C71 ( PascalFrancis/Corpus ); précédent : 000C70; suivant : 000C72

Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices

Auteurs : F. Simonot ; Y. Q. Song

Source :

Journal of applied probability [ 0021-9002 ] ; 1996.

RBID : Pascal:97-0227616

Descripteurs français

Pascal (Inist)
- Matrice stochastique, Chaîne Markov, Loi limite, Taux convergence, Processus stationnaire.

English descriptors

KwdEn :
- Convergence rate, Limit distribution, Markov chain, Stationary process, Stochastic matrix.

Abstract

Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and P_n be any n x n stochastic matrix with P_n≥ T_n' where T_n denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and π_n for P and P_n 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 π_n to π can be expressed in terms of the radius of convergence of the generating function of π. 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 (Aim)) is such that we can find a real number r_o > 1 with E(r^A₀) = 1, then the exact convergence rate of π_n to π is characterized by r_o. Moreover, when the generating function of A is not defined for |z| > 1, we derive an upper bound for the distance between π_n and π based on the moments of A.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A02	`01`			`@0 JPRBAM`
A03		`1`		`@0 J. appl. probab.`
A05				`@2 33`
A06				`@2 4`
A08	`01`	`1`	`ENG`	`@1 Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices`
A11	`01`	`1`		`@1 SIMONOT (F.)`
A11	`02`	`1`		`@1 SONG (Y. Q.)`
A14	`01`			`@1 Université Henri Poincaré @3 FRA @Z 1 aut.`
A14	`02`			`@1 CRIN-ENSEM @3 FRA @Z 2 aut.`
A20				`@1 974-985`
A21				`@1 1996`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 12216 @5 354000062831220070`
A44				`@0 0000 @1 © 1997 INIST-CNRS. All rights reserved.`
A45				`@0 20 ref.`
A47	`01`	`1`		`@0 97-0227616`
A60				`@1 P`
A61				`@0 A`
A64	`01`	`1`		`@0 Journal of applied probability`
A66	`01`			`@0 GBR`
C01	`01`		`ENG`	@0 Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and P_n be any n x n stochastic matrix with P_n≥ T_n' where T_n denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and π_n for P and P_n 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 π_n to π can be expressed in terms of the radius of convergence of the generating function of π. 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 (Aim)) is such that we can find a real number r_o > 1 with E(r^A₀) = 1, then the exact convergence rate of π_n to π is characterized by r_o. Moreover, when the generating function of A is not defined for \|z\| > 1, we derive an upper bound for the distance between π_n and π based on the moments of A.
C02	`01`	`X`		`@0 001A02H01J`
C02	`02`	`X`		`@0 001A02H01K`
C03	`01`	`X`	`FRE`	`@0 Matrice stochastique @5 01`
C03	`01`	`X`	`ENG`	`@0 Stochastic matrix @5 01`
C03	`01`	`X`	`SPA`	`@0 Matriz estocástica @5 01`
C03	`02`	`X`	`FRE`	`@0 Chaîne Markov @5 02`
C03	`02`	`X`	`ENG`	`@0 Markov chain @5 02`
C03	`02`	`X`	`SPA`	`@0 Cadena Markov @5 02`
C03	`03`	`X`	`FRE`	`@0 Loi limite @5 03`
C03	`03`	`X`	`ENG`	`@0 Limit distribution @5 03`
C03	`03`	`X`	`SPA`	`@0 Ley límite @5 03`
C03	`04`	`X`	`FRE`	`@0 Taux convergence @5 04`
C03	`04`	`X`	`ENG`	`@0 Convergence rate @5 04`
C03	`04`	`X`	`SPA`	`@0 Relación convergencia @5 04`
C03	`05`	`X`	`FRE`	`@0 Processus stationnaire @5 05`
C03	`05`	`X`	`ENG`	`@0 Stationary process @5 05`
C03	`05`	`X`	`SPA`	`@0 Proceso estacionario @5 05`
N21				`@1 118`

Format Inist (serveur)

NO :	PASCAL 97-0227616 INIST
ET :	Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices
AU :	SIMONOT (F.); SONG (Y. Q.)
AF :	Université Henri Poincaré/France (1 aut.); CRIN-ENSEM/France (2 aut.)
DT :	Publication en série; Niveau analytique
SO :	Journal of applied probability; ISSN 0021-9002; Coden JPRBAM; Royaume-Uni; Da. 1996; Vol. 33; No. 4; Pp. 974-985; Bibl. 20 ref.
LA :	Anglais
EA :	Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and P_n be any n x n stochastic matrix with P_n≥ T_n' where T_n denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and π_n for P and P_n 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 π_n to π can be expressed in terms of the radius of convergence of the generating function of π. 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 (Aim)) is such that we can find a real number r_o > 1 with E(r^A₀) = 1, then the exact convergence rate of π_n to π is characterized by r_o. Moreover, when the generating function of A is not defined for \|z\| > 1, we derive an upper bound for the distance between π_n and π based on the moments of A.
CC :	001A02H01J; 001A02H01K
FD :	Matrice stochastique; Chaîne Markov; Loi limite; Taux convergence; Processus stationnaire
ED :	Stochastic matrix; Markov chain; Limit distribution; Convergence rate; Stationary process
SD :	Matriz estocástica; Cadena Markov; Ley límite; Relación convergencia; Proceso estacionario
LO :	INIST-12216.354000062831220070
ID :	97-0227616

Links to Exploration step

Pascal:97-0227616

Le document en format XML

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<front><div type="abstract" xml:lang="en">Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and P<sub>n</sub>
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 where T<sub>n</sub>
 denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and π<sub>n</sub>
 for P and P<sub>n</sub>
 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 π<sub>n</sub>
 to π can be expressed in terms of the radius of convergence of the generating function of π. 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 (Aim)) is such that we can find a real number r<sub>o</sub>
 > 1 with E(r<sup>A</sup>
<sub>0</sub>
) = 1, then the exact convergence rate of π<sub>n</sub>
 to π is characterized by r<sub>o</sub>
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 where T<sub>n</sub>
 denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and π<sub>n</sub>
 for P and P<sub>n</sub>
 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 π<sub>n</sub>
 to π can be expressed in terms of the radius of convergence of the generating function of π. 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 (Aim)) is such that we can find a real number r<sub>o</sub>
 > 1 with E(r<sup>A</sup>
<sub>0</sub>
) = 1, then the exact convergence rate of π<sub>n</sub>
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<server><NO>PASCAL 97-0227616 INIST</NO>
<ET>Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices</ET>
<AU>SIMONOT (F.); SONG (Y. Q.)</AU>
<AF>Université Henri Poincaré/France (1 aut.); CRIN-ENSEM/France (2 aut.)</AF>
<DT>Publication en série; Niveau analytique</DT>
<SO>Journal of applied probability; ISSN 0021-9002; Coden JPRBAM; Royaume-Uni; Da. 1996; Vol. 33; No. 4; Pp. 974-985; Bibl. 20 ref.</SO>
<LA>Anglais</LA>
<EA>Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and P<sub>n</sub>
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 where T<sub>n</sub>
 denotes the n x n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and π<sub>n</sub>
 for P and P<sub>n</sub>
 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 π<sub>n</sub>
 to π can be expressed in terms of the radius of convergence of the generating function of π. 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 (Aim)) is such that we can find a real number r<sub>o</sub>
 > 1 with E(r<sup>A</sup>
<sub>0</sub>
) = 1, then the exact convergence rate of π<sub>n</sub>
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Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices

Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices

Source :

Descripteurs français

English descriptors

Abstract

Notice en format standard (ISO 2709)

Format Inist (serveur)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri