Abstract
A time-inhomogeneous Feller-type diffusion process with linear infinitesimal drift alpha (t)x+beta (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 beta (t) and the noise intensity function r(t) are connected via the relation beta (t)=xi ,r(t), with 0le xi <1. Various numerical computations are performed to illustrate the effect of the parameters on the first-passage time density, by assuming that alpha (t), beta (t) or both of these functions exhibit some kind of periodicity.
Highlights
Introduction and BackgroundOne-dimensional time-inhomogeneous diffusion processes play a relevant role in different application fields, including physics, biology, neuroscience, finance and others
We consider a timeinhomogeneous Feller-type diffusion process, characterized by linear infinitesimal drift and linear infinitesimal variance vanishing in the zero-state
The explicit expressions of the transition pdf and of the first-passage time (FPT) density through the zero-state are obtained in the proportional case
Summary
One-dimensional time-inhomogeneous diffusion processes play a relevant role in different application fields, including physics, biology, neuroscience, finance and others (cf., for instance, Giorno and Nobile [1,2], Albano and Giorno [3], Ghost and Prajneshu [4], Buonocore et al [5], Gutiérrez et al [6], Di Crescenzo et al [7], Román-Román et al [8], Molini et al [9], Gan and Waxman [10], Abundo [11]). We consider a timeinhomogeneous Feller-type diffusion process, characterized by linear infinitesimal drift and linear infinitesimal variance vanishing in the zero-state (lower boundary of the process). We assume that the zero-state represents an absorbing boundary for the process
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