Strong stationary duality for continuous-time Markov chains. I: Theory

DOI10.1007/BF01046778zbMath0746.60075OpenAlexW2047675471MaRDI QIDQ1185795

James Allen Fill

Publication date: 28 June 1992

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01046778

zbMATH Keywords

continuous-time Markov chainbirth-death processesvariation distancerandomized stopping timemonotone likelihood chains

Mathematics Subject Classification ID

Continuous-time Markov processes on discrete state spaces (60J27)

Related Items

On hitting times and fastest strong stationary times for skip-free and more general chains ⋮ On times to quasi-stationarity for birth and death processes ⋮ The passage time distribution for a birth-and-death chain: Strong stationary duality gives a first stochastic proof ⋮ The birth-death processes with regular boundary: stationarity and quasi-stationarity ⋮ Hitting time distributions for denumerable birth and death processes ⋮ Spectral computations for birth and death chains ⋮ Factorized duality, stationary product measures and generating functions ⋮ Change of measure in the lookdown particle system ⋮ Unnamed Item ⋮ Hitting times and interlacing eigenvalues: a stochastic approach using intertwinings ⋮ On the notion(s) of duality for Markov processes ⋮ Strong stationary duality for diffusion processes ⋮ Explicit criteria on separation cutoff for birth and death chains ⋮ Separation cut-offs for birth and death chains ⋮ Existence condition of strong stationary times for continuous time Markov chains on discrete graphs ⋮ On absorption times and Dirichlet eigenvalues ⋮ On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes ⋮ Computable Bounds on the Spectral Gap for Unreliable Jackson Networks

Cites Work

• Unnamed Item
• Unnamed Item
• Strong stationary times via a new form of duality
• Denumerable Markov processes and the associated contraction semigroups on l
• Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process
• Geometric bounds for eigenvalues of Markov chains
• The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes
• Examples for the Theory of Strong Stationary Duality with Countable State Spaces
• Time to Stationarity for a Continuous-Time Markov Chain
• Stochastic monotonicity of birth–death processes