The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α(t)x+ β(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 α(t), β(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.
Time-inhomogeneous Feller-type diffusion process in population dynamics
Virginia Giorno;Nobile Amelia Giuseppina
2021-01-01
Abstract
The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α(t)x+ β(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 α(t), β(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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
