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Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics

Author

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  • Virginia Giorno

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

Abstract

The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α ( t ) x + β ( t ) and infinitesimal variance 2 r ( t ) x , with a zero-flux condition in the zero-state, is considered. This process is obtained as a continuous approximation of a birth-death process with immigration. The transition probability density function and the related conditional moments, with their asymptotic behaviors, are determined. Special attention is paid to the cases in which the intensity functions α ( t ) , β ( t ) , r ( t ) exhibit some kind of periodicity due to seasonal immigration, regular environmental cycles or random fluctuations. Various numerical computations are performed to illustrate the role played by the periodic functions.

Suggested Citation

  • Virginia Giorno & Amelia G. Nobile, 2021. "Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics," Mathematics, MDPI, vol. 9(16), pages 1-29, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1879-:d:610197
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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. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Tian, Yingxu & Zhang, Haoyan, 2018. "Skew CIR process, conditional characteristic function, moments and bond pricing," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 230-238.
    4. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109, January.
    5. Di Nardo, Elvira & D’Onofrio, Giuseppe, 2021. "A cumulant approach for the first-passage-time problem of the Feller square-root process," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    6. Peng, Qidi & Schellhorn, Henry, 2018. "On the distribution of extended CIR model," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 23-29.
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