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On the Exact Solution of a Generalized Polya Process

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  • Hidetoshi Konno

Abstract

There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems.

Suggested Citation

  • Hidetoshi Konno, 2010. "On the Exact Solution of a Generalized Polya Process," Advances in Mathematical Physics, Hindawi, vol. 2010, pages 1-12, November.
    • Handle: RePEc:hin:jnlamp:504267
    DOI: 10.1155/2010/504267
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    Cited by:

    1. Virginia Giorno & Amelia G. Nobile, 2020. "Bell Polynomial Approach for Time-Inhomogeneous Linear Birth–Death Process with Immigration," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    2. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1627-1650, September.
    3. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    4. Asadi, Majid, 2023. "On a parametric model for the mean number of system repairs with applications," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    5. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On Properties of the Phase-type Mixed Poisson Process and its Applications to Reliability Shock Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2933-2960, December.
    6. Lina Bian & Bo Peng & Yong Ye, 2023. "Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model," Mathematics, MDPI, vol. 11(21), pages 1-19, November.
    7. Kerry Fendick & Ward Whitt, 2022. "Heavy traffic limits for queues with non-stationary path-dependent arrival processes," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 113-135, June.

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