Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach

被引：0

作者：

Castro, Matheus M. ^{[1
]}

Lamb, Jeroen S. W. ^{[1
,2
,3
]}

Olicon-Mendez, Guillermo ^{[4
]}

Rasmussen, Martin ^{[1
]}

机构：

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Univ Tokyo, Int Res Ctr Neurointelligence, Tokyo 1130033, Japan

[3] Gulf Univ Sci & Technol, Ctr Appl Math & Bioinformat, Dept Math & Nat Sci, Halwally, Kuwait

[4] Univ Potsdam, Inst Math, Karl Liebknecht Str 24-25, D-14476 Potsdam, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2024年 / 173卷

基金：

英国工程与自然科学研究理事会; 巴西圣保罗研究基金会;

关键词：

Markov chains with absorption; Banach lattice; Quasi-stationary measure; Quasi-ergodic measure; Yaglom limit; ONE-DIMENSIONAL DIFFUSIONS; DISTRIBUTIONS; TIME; CONVERGENCE; LIMITS;

D O I：

10.1016/j.spa.2024.104364

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish the existence and uniqueness of quasi -stationary and quasi-ergodic measures for almost surely absorbed discrete -time Markov chains under weak conditions. We obtain our results by exploiting Banach lattice properties of transition functions under natural regularity assumptions.

引用

页数：19

共 36 条

[1] Quasi-ergodic limits for finite absorbing Markov chains
Colonius, Fritz
Rasmussen, Martin
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 609 : 253 - 288
[2] On the quasi-ergodic distribution of absorbing Markov processes
He, Guoman
Zhang, Hanjun
Zhu, Yixia
[J]. STATISTICS & PROBABILITY LETTERS, 2019, 149 : 116 - 123
[3] QUASI-STATIONARY DISTRIBUTIONS FOR ABSORBING CONTINUOUS-TIME DENUMERABLE MARKOV CHAINS
FLASPOHLER, DC
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1974, 26 (02) : 351 - 356
[4] ON QUASI-STATIONARY DISTRIBUTIONS IN ABSORBING CONTINUOUS-TIME FINITE MARKOV CHAINS
DARROCH, JN
SENETA, E
[J]. JOURNAL OF APPLIED PROBABILITY, 1967, 4 (01) : 192 - &
[5] Existence and Uniqueness of Quasi-stationary Distributions for Symmetric Markov Processes with Tightness Property
Takeda, Masayoshi
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2019, 32 (04) : 2006 - 2019
[6] Existence and Uniqueness of Quasi-stationary Distributions for Symmetric Markov Processes with Tightness Property
Masayoshi Takeda
[J]. Journal of Theoretical Probability, 2019, 32 : 2006 - 2019
[7] Approximations of quasi-stationary distributions for Markov chains
Breyer, LA
Hart, AG
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2000, 31 (10-12) : 69 - 79
[8] MOMENTS FOR STATIONARY AND QUASI-STATIONARY DISTRIBUTIONS OF MARKOV-CHAINS
SENETA, E
TWEEDIE, RL
[J]. JOURNAL OF APPLIED PROBABILITY, 1985, 22 (01) : 148 - 155
[9] Further results on the relationship between μ-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains
Elmes, S
Pollett, P
Walker, D
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2000, 31 (10-12) : 107 - 113
[10] ON THE EXISTENCE OF QUASI-STATIONARY DISTRIBUTIONS IN DENUMERABLE R-TRANSIENT MARKOV-CHAINS
KIJIMA, M
[J]. JOURNAL OF APPLIED PROBABILITY, 1992, 29 (01) : 21 - 36

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