Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions

Virginia Giorno and Amelia G. Nobile
Additional contact information
Virginia Giorno: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy
Amelia G. Nobile: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy

Mathematics, 2019, vol. 7, issue 6, 1-19

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.

Keywords: diffusion processes; first-passage time; population dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/6/555/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/6/555/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:6:p:555-:d:240861

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().