Monotone infinite stochastic matrices and their augmented truncations

DOI10.1016/0304-4149(87)90019-6zbMath0623.60089OpenAlexW2076457397MaRDI QIDQ1091679

Eugene Seneta, Diana Gibson

Publication date: 1987

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(87)90019-6

zbMATH Keywords

tightnessstochastic matrixirreducible and positive recurrentstochastically monotone

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Stochastic matrices (15B51)

Related Items (13)

Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines ⋮ On the approximation of the stationary distribution of a monotone stochastic Markov chain ⋮ Continuous-time block-monotone Markov chains and their block-augmented truncations ⋮ Weak stability bounds for approximations of invariant measures with applications to queueing ⋮ Error bounds for augmented truncation approximations of continuous-time Markov chains ⋮ Stochastic monotonicity and comparability of Markov chains with block-monotone transition matrices and their applications to queueing systems ⋮ Strong truncation approximation in tandem queues with blocking ⋮ A pathwise approach to the extinction of branching processes with countably many types ⋮ A weak perturbation theory for approximations of invariant measures in M/G/1 model ⋮ Stationary Distributions of Continuous-Time Markov Chains: A Review of Theory and Truncation-Based Approximations ⋮ Augmented truncation approximations of discrete-time Markov chains ⋮ Effect of energy-saving server scheduling on power consumption for large-scale data centers ⋮ Error Bounds for Augmented Truncations of Discrete-Time Block-Monotone Markov Chains under Geometric Drift Conditions

Cites Work

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• Iterative aggregation: convergence rate
• Convergence of quasi-stationary distributions in birth-death processes
• Non-negative matrices and Markov chains. 2nd ed
• Computing the stationary distribution for infinite Markov chains
• The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes
• Monotone matrices and monotone Markov processes
• Convergence of quasi-stationary to stationary distributions for stochastically monotone Markov processes
• Augmented truncations of infinite stochastic matrices
• Approximation of the invariant probability measure of an infinite stochastic matrix
• Stochastically monotone Markov Chains

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