Abstract
AbstractA time-inhomogeneous Feller-type diffusion process with linear infinitesimal drift $$\alpha (t)x+\beta (t)$$
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 $$\beta (t)$$
β
(
t
)
and the noise intensity function r(t) are connected via the relation $$\beta (t)=\xi \,r(t)$$
β
(
t
)
=
ξ
r
(
t
)
, with $$0\le \xi <1$$
0
≤
ξ
<
1
. Various numerical computations are performed to illustrate the effect of the parameters on the first-passage time density, by assuming that $$\alpha (t)$$
α
(
t
)
, $$\beta (t)$$
β
(
t
)
or both of these functions exhibit some kind of periodicity.
Funder
Università degli Studi di Salerno
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
3 articles.
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