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The decay function of nonhomogeneous birth-death processes, with application to mean-field models

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  • Granovsky, Boris L.
  • Zeifman, Alexander I.

Abstract

The paper develops in different directions the method of the second author for estimation of the rate of exponential convergence of nonhomogeneous birth-death processes. Applying the method to mean-field models, we discover some phenomena related to their spectral gaps.

Suggested Citation

  • Granovsky, Boris L. & Zeifman, Alexander I., 1997. "The decay function of nonhomogeneous birth-death processes, with application to mean-field models," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 105-120, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:105-120
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    References listed on IDEAS

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    1. Granovsky, Boris L. & Madras, Neal, 1995. "The noisy voter model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 23-43, January.
    2. Zeifman, A.I., 1995. "Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 157-173, September.
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    Cited by:

    1. Zeifman, A.I. & Satin, Y.A. & Kiseleva, K.M., 2020. "On obtaining sharp bounds of the rate of convergence for a class of continuous-time Markov chains," Statistics & Probability Letters, Elsevier, vol. 161(C).
    2. Korolev, V.Yu. & Chertok, A.V. & Korchagin, A.Yu. & Zeifman, A.I., 2015. "Modeling high-frequency order flow imbalance by functional limit theorems for two-sided risk processes," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 224-241.
    3. Zeifman, A.I. & Korolev, V. Yu., 2015. "Two-sided bounds on the rate of convergence for continuous-time finite inhomogeneous Markov chains," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 30-36.
    4. Zeifman, A.I. & Korolev, V.Yu. & Satin, Ya.A. & Kiseleva, K.M., 2018. "Lower bounds for the rate of convergence for continuous-time inhomogeneous Markov chains with a finite state space," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 84-90.
    5. Erik Doorn, 2011. "Rate of convergence to stationarity of the system M/M/N/N+R," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 336-350, December.

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