IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i6p555-d240861.html
   My bibliography  Save this article

Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions

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 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/6/555/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/6/555/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giorno, Virginia & Román-Román, Patricia & Spina, Serena & Torres-Ruiz, Francisco, 2017. "Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 18-31.
    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. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).
    4. Kulmus, Kathrin & Essex, Christopher & Prehl, Janett & Hoffmann, Karl Heinz, 2019. "The entropy production paradox for fractional master equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1370-1378.
    5. Albano, G. & Giorno, V., 2020. "Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    6. M’hamed Gaïgi & Idris Kharroubi & Thomas Lim, 2020. "Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints," Mathematics, MDPI, vol. 8(11), pages 1-25, November.
    7. Antonio Di Crescenzo & Paola Paraggio & Serena Spina, 2023. "Stochastic Growth Models for the Spreading of Fake News," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    8. Fabien Campillo & Marc Joannides & Irène Larramendy-Valverde, 2016. "Analysis and Approximation of a Stochastic Growth Model with Extinction," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 499-515, June.
    9. Zhongda, Tian & Shujiang, Li & Yanhong, Wang & Yi, Sha, 2017. "A prediction method based on wavelet transform and multiple models fusion for chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 158-172.
    10. Virginia Giorno & Amelia G. Nobile, 2021. "On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes," Mathematics, MDPI, vol. 9(8), pages 1-25, April.
    11. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    12. 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.
    13. Correale, T.G. & Monteiro, L.H.A., 2016. "On the dynamics of axonal membrane: Ion channel as the basic unit of a deterministic model," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 292-302.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:555-:d:240861. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.