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On a class of birth-death processes with time-varying intensity functions

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  • Giorno, Virginia
  • Nobile, Amelia G.

Abstract

In this paper, we investigate on a class of time-inhomogeneous birth-death chains obtained by applying the composition method to two time-inhomogeneous double-ended chains. Then, we consider the corresponding restricted birth-death process, with zero reflecting boundary. Finally, starting from the restricted process, we construct a time-inhomogeneous BD chain symmetric with respect to zero-state. We obtain closed form expressions for the transition probabilities and for the conditional moments; furthermore, the first-passage-time problem is also taken in consideration. Finally, various numerical computations are performed for periodic intensity functions.

Suggested Citation

  • Giorno, Virginia & Nobile, Amelia G., 2020. "On a class of birth-death processes with time-varying intensity functions," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    • Handle: RePEc:eee:apmaco:v:379:y:2020:i:c:s0096300320302241
    DOI: 10.1016/j.amc.2020.125255
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    Cited by:

    1. 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).
    2. 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).
    3. Giorno, Virginia & Nobile, Amelia G., 2023. "On a time-inhomogeneous diffusion process with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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