On the Construction of Some Fractional Stochastic Gompertz Models

Giacomo Ascione and Enrica Pirozzi
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Giacomo Ascione: Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universitá degli Studi di Napoli Federico II, I-80126 Naples, Italy
Enrica Pirozzi: Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universitá degli Studi di Napoli Federico II, I-80126 Naples, Italy

Mathematics, 2020, vol. 8, issue 1, 1-24

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.

Keywords: Caputo fractional derivative; Gaussian processes; fractional-integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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