A time-inhomogeneous Feller-type diffusion process with linear infinitesimal drift α(t)x + β(t) and linear infinitesimal variance 2r(t)x is considered. For this process, the transition density in the presence of an absorbing boundary in the zero-state and the first-passage time density through the zero-state are obtained. Special attention is dedicated to the proportional case, in which the immigration intensity function β (t ) and the noise intensity function r (t ) are connected via the relation β(t) = ξ r(t), with 0 ≤ ξ < 1. Various numerical computations are performed to illustrate the effect of the parameters on the first-passage time density, by assuming that α(t), β(t) or both of these functions exhibit some kind of periodicity.
Time-Inhomogeneous Feller-type Diffusion Process with Absorbing Boundary Condition
Giorno Virginia;Nobile Amelia Giuseppina
2021
Abstract
A time-inhomogeneous Feller-type diffusion process with linear infinitesimal drift α(t)x + β(t) and linear infinitesimal variance 2r(t)x is considered. For this process, the transition density in the presence of an absorbing boundary in the zero-state and the first-passage time density through the zero-state are obtained. Special attention is dedicated to the proportional case, in which the immigration intensity function β (t ) and the noise intensity function r (t ) are connected via the relation β(t) = ξ r(t), with 0 ≤ ξ < 1. Various numerical computations are performed to illustrate the effect of the parameters on the first-passage time density, by assuming that α(t), β(t) or both of these functions exhibit some kind of periodicity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
