Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics

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

Mathematics, 2021, vol. 9, issue 16, 1-29

Abstract: The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift ? ( t ) x + ? ( t ) and infinitesimal variance 2 r ( t ) x , with a zero-flux condition in the zero-state, is considered. This process is obtained as a continuous approximation of a birth-death process with immigration. The transition probability density function and the related conditional moments, with their asymptotic behaviors, are determined. Special attention is paid to the cases in which the intensity functions ? ( t ) , ? ( t ) , r ( t ) exhibit some kind of periodicity due to seasonal immigration, regular environmental cycles or random fluctuations. Various numerical computations are performed to illustrate the role played by the periodic functions.

Keywords: diffusion approximation; transient and asymptotic densities; conditional moments; periodic intensity functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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