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Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions

Author

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  • 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 consider two different time-inhomogeneous diffusion processes useful to model the evolution of a population in a random environment. The first is a Gompertz-type diffusion process with time-dependent growth intensity, carrying capacity and noise intensity, whose conditional median coincides with the deterministic solution. The second is a shifted-restricted Gompertz-type diffusion process with a reflecting condition in zero state and with time-dependent regulation functions. For both processes, we analyze the transient and the asymptotic behavior of the transition probability density functions and their conditional moments. Particular attention is dedicated to the first-passage time, by deriving some closed form for its density through special boundaries. Finally, special cases of periodic regulation functions are discussed.

Suggested Citation

  • Virginia Giorno & Amelia G. Nobile, 2019. "Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions," Mathematics, MDPI, vol. 7(6), pages 1-19, June.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:555-:d:240861
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    References listed on IDEAS

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    1. Albano, Giuseppina & Giorno, Virginia & Román-Román, Patricia & Torres-Ruiz, Francisco, 2012. "Inference on a stochastic two-compartment model in tumor growth," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1723-1736.
    2. Christos H. Skiadas, 2010. "Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 261-270, June.
    3. Antonio Di Crescenzo & Paola Paraggio, 2019. "Logistic Growth Described by Birth-Death and Diffusion Processes," Mathematics, MDPI, vol. 7(6), pages 1-28, May.
    4. Buonocore, A. & Caputo, L. & Nobile, A.G. & Pirozzi, E., 2014. "Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 799-809.
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    Cited by:

    1. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    2. Giorno, Virginia & Nobile, Amelia G., 2023. "On a time-inhomogeneous diffusion process with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    3. Antonio Di Crescenzo & Paola Paraggio & Patricia Román-Román & Francisco Torres-Ruiz, 2023. "Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean," Statistical Papers, Springer, vol. 64(5), pages 1391-1438, October.

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