IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v72y1997i1p105-120.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00085-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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).
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. André de Palma & Claude Lefèvre, 2018. "Bottleneck models and departure time problems," Working Papers hal-01581519, HAL.
    2. Zeifman, A.I. & Korolev, V.Yu., 2014. "On perturbation bounds for continuous-time Markov chains," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 66-72.
    3. Peralta, Antonio F. & Khalil, Nagi & Toral, Raúl, 2020. "Ordering dynamics in the voter model with aging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    4. Kononovicius, Aleksejus, 2021. "Supportive interactions in the noisy voter model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Ted Theodosopoulos, 2004. "Uncertainty relations in models of market microstructure," Papers math/0409076, arXiv.org, revised Feb 2005.
    6. Yacov Satin & Rostislav Razumchik & Ivan Kovalev & Alexander Zeifman, 2023. "Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    7. Khalil, Nagi & Toral, Raúl, 2019. "The noisy voter model under the influence of contrarians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 81-92.
    8. 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.
    9. 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.
    10. Yacov Satin & Alexander Zeifman & Alexander Sipin & Sherif I. Ammar & Janos Sztrik, 2020. "On Probability Characteristics for a Class of Queueing Models with Impatient Customers," Mathematics, MDPI, vol. 8(4), pages 1-15, April.
    11. 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.
    12. Kyrylo Shmatov & Mikhail Smirnov, 2005. "On Some Processes and Distributions in a Collective Model of Investors' Behavior," Papers nlin/0506015, arXiv.org.
    13. Adri'an Carro & Ra'ul Toral & Maxi San Miguel, 2016. "The noisy voter model on complex networks," Papers 1602.06935, arXiv.org, revised Apr 2016.
    14. Volker Hösel & Johannes Müller & Aurelien Tellier, 2019. "Universality of neutral models: decision process in politics," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-8, December.
    15. Zeifman, A. & Satin, Y. & Kiseleva, K. & Korolev, V. & Panfilova, T., 2019. "On limiting characteristics for a non-stationary two-processor heterogeneous system," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 48-65.
    16. Alexander Zeifman & Yacov Satin & Ksenia Kiseleva & Victor Korolev, 2019. "On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    17. Satin, Y.A. & Razumchik, R.V. & Zeifman, A.I. & Kovalev, I.A., 2022. "Upper bound on the rate of convergence and truncation bound for non-homogeneous birth and death processes on Z," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    18. 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.
    19. Theodosopoulos, Ted, 2005. "Uncertainty relations in models of market microstructure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 209-216.
    20. Alili, Smail & Ignatiouk-Robert, Irina, 2001. "On the surviving probability of an annihilating branching process and application to a nonlinear voter model," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 301-316, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:105-120. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.