Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes

DOI10.1016/0304-4149(95)00028-6zbMath0846.60084OpenAlexW2090214931MaRDI QIDQ1904541

Alexander I. Zejfman

Publication date: 23 September 1996

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

Full work available at URL: https://doi.org/10.1016/0304-4149(95)00028-6

zbMATH Keywords

rate of convergenceergodicitydifferential equationsboundsbirth and death process

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Continuous-time Markov processes on discrete state spaces (60J27)

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Cites Work

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• On the largest negative eigenvalue of the infinitesimal generator associated with M/M/n/n queues
• Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tri-diagonal matrices
• On exponential ergodicity and spectral structure for birth-death processes. II
• Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process
• A note on coupling of birth and death processes
• Some estimates of the rate of convergence for birth and death processes
• Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes
• Evaluation of the decay parameter for some specialized birth-death processes
• On the estimation of probabilities for birth and death processes

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