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On the Construction of Some Fractional Stochastic Gompertz Models

Author

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  • Giacomo Ascione

    (Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universitá degli Studi di Napoli Federico II, I-80126 Naples, Italy
    These authors contributed equally to this work.)

  • Enrica Pirozzi

    (Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universitá degli Studi di Napoli Federico II, I-80126 Naples, Italy
    These authors contributed equally to this work.)

Abstract

The aim of this paper is the construction of stochastic versions for some fractional Gompertz curves. To do this, we first study a class of linear fractional-integral stochastic equations, proving existence and uniqueness of a Gaussian solution. Such kinds of equations are then used to construct fractional stochastic Gompertz models. Finally, a new fractional Gompertz model, based on the previous two, is introduced and a stochastic version of it is provided.

Suggested Citation

  • Giacomo Ascione & Enrica Pirozzi, 2020. "On the Construction of Some Fractional Stochastic Gompertz Models," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:60-:d:304441
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
    2. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    3. De Lauro, E. & De Martino, S. & De Siena, S. & Giorno, V., 2014. "Stochastic roots of growth phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 207-213.
    4. Anh, P.T. & Doan, T.S. & Huong, P.T., 2019. "A variation of constant formula for Caputo fractional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 351-358.
    5. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
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