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Bell Polynomial Approach for Time-Inhomogeneous Linear Birth–Death Process with Immigration

Author

Listed:
  • Virginia Giorno

    (Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy
    These authors contributed equally to this work.)

  • Amelia G. Nobile

    (Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy
    These authors contributed equally to this work.)

Abstract

We considered the time-inhomogeneous linear birth–death processes with immigration. For these processes closed form expressions for the transition probabilities were obtained in terms of the complete Bell polynomials. The conditional mean and the conditional variance were explicitly evaluated. Several time-inhomogeneous processes were studied in detail in view of their potential applications in population growth models and in queuing systems. A time-inhomogeneous linear birth–death processes with finite state-space was also taken into account. Special attention was devoted to the cases of periodic immigration intensity functions that play an important role in the description of the evolution of dynamic systems influenced by seasonal immigration or other regular environmental cycles. Various numerical computations were performed for periodic immigration intensity functions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1123-:d:382293
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    References listed on IDEAS

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    1. Antonio Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2012. "A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 937-954, December.
    2. Hidetoshi Konno, 2010. "On the Exact Solution of a Generalized Polya Process," Advances in Mathematical Physics, Hindawi, vol. 2010, pages 1-12, November.
    3. Yacov Satin & Alexander Zeifman & Anastasia Kryukova, 2019. "On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model," Mathematics, MDPI, vol. 7(8), pages 1-11, July.
    4. Di Crescenzo, Antonio & Giorno, Virginia & Nobile, Amelia G., 2016. "Constructing transient birth–death processes by means of suitable transformations," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 152-171.
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    Cited by:

    1. Ilya Usov & Yacov Satin & Alexander Zeifman & Victor Korolev, 2022. "Ergodicity Bounds and Limiting Characteristics for a Modified Prendiville Model," Mathematics, MDPI, vol. 10(23), pages 1-14, November.
    2. 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).

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