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Distributions in the Ehrenfest process

Author

Listed:
  • Balaji, Srinivasan
  • Mahmoud, Hosam M.
  • Watanabe, Osamu

Abstract

The quest continues for cases of interest where the differential equations for the Pólya process are amenable to an asymptotic solution. We introduce a tenable class of urns that generalize the classical Ehrenfest model, and analyze the Ehrenfest process obtained by embedding the discrete evolution in real time. We show that lurking under the Ehrenfest process is a limiting binomial distribution, whose number of trials is an integer invariant property of the process.

Suggested Citation

  • Balaji, Srinivasan & Mahmoud, Hosam M. & Watanabe, Osamu, 2006. "Distributions in the Ehrenfest process," Statistics & Probability Letters, Elsevier, vol. 76(7), pages 666-674, April.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:7:p:666-674
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    Citations

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    Cited by:

    1. Rafik Aguech & Hanene Mohamed, 2023. "A Continuous-Time Urn Model for a System of Activated Particles," Mathematics, MDPI, vol. 11(24), pages 1-13, December.
    2. Jun-ya Gotoh & Hui Jin & Ushio Sumita, 2011. "Numerical Evaluation of Dynamic Behavior of Ornstein–Uhlenbeck Processes Modified by Various Boundaries and its Application to Pricing Barrier Options," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 193-219, March.
    3. Chen Chen & Hosam Mahmoud, 2018. "The continuous-time triangular Pólya process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 303-321, April.
    4. Sparks, Joshua & Mahmoud, Hosam M., 2013. "Phases in the two-color tenable zero-balanced Pólya process," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 265-271.

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