153 research outputs found
Time-Inhomogeneous Feller-type Diffusion Process with Absorbing Boundary Condition
AbstractA 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
)
=
Îľ
r
(
t
)
, with
0
≤
Îľ
<
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
Exact solutions and asymptotic behaviors for the reflected Wiener, Ornstein-Uhlenbeck and Feller diffusion processes
We analyze the transition probability density functions in the presence of a zero-flux condition in the zero-state and their asymptotic behaviors for the Wiener, Ornstein Uhlenbeck and Feller diffusion processes. Particular attention is paid to the time-inhomogeneous proportional cases and to the time-homogeneous cases. A detailed study of the moments of first-passage time and of their asymptotic behaviors is carried out for the time-homogeneous cases. Some relationships between the transition probability density functions for the restricted Wiener, Ornstein-Uhlenbeck and Feller processes are proved. Specific applications of the results to queueing systems are provided
Inference on a stochastic two-compartment model in tumor growth
A continuous-time model that incorporates several key elements in tumor dynamics is analyzed. More precisely, the form of proliferating and quiescent cell lines comes out from their relations with the whole tumor mass, giving rise to a two-dimensional diffusion process, generally time non-homogeneous. This model is able to include the effects of the mutual interactions between the two subpopulations. Estimation of the rates of the two subpopulations based on some characteristics of the involved diffusion processes is discussed when longitudinal data are available. To this aim, two procedures are presented. Some simulation results are developed in order to show the validity of these procedures as well as to compare them. An application to real data is finally presented
A new approach to the construction of first-passage-time densities
A new method for constructing first-passage-time probability density functions is outlined. This rests on the possibility of constructing the transition p.d.f. of a new diffusion process in terms of a preassigned transition p.d.f. without making use of the classical space-time transformations of the Kolmogorov equation. A few examples are finally discusse
Study of a general growth model
We discuss a general growth curve including several parameters, whose choice leads to a variety of models including the classical cases of Malthusian, Richards, Gompertz, Logistic and some their generalizations. The advantage is to obtain a single mathematically tractable equation from which the main characteristics of the considered curves can be deduced. We focus on the effects of the involved parameters through both analytical results and computational evaluations
Inference on an heterocedastic Gompertz tumor growth model
We consider a non homogeneous Gompertz diffusion process whose parameters are modified by generally time-dependent exogenous factors included in the infinitesimal moments. The proposed model is able to describe tumor dynamics under the effect of anti-proliferative and/or cell death-induced therapies. We assume that such therapies can modify also the infinitesimal variance of the diffusion process. An estimation procedure, based on a control group and two treated groups, is proposed to infer the model by estimating the constant parameters and the time-dependent terms. Moreover, several concatenated hypothesis tests are considered in order to confirm or reject the need to include time-dependent functions in the infinitesimal moments. Simulations are provided to evaluate the efficiency of the suggested procedures and to validate the testing hypothesis. Finally, an application to real data is considered
A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation
Consider a system performing a continuous-time random walk on the integers,
subject to catastrophes occurring at constant rate, and followed by
exponentially-distributed repair times. After any repair the system starts anew
from state zero. We study both the transient and steady-state probability laws
of the stochastic process that describes the state of the system. We then
derive a heavy-traffic approximation to the model that yields a jump-diffusion
process. The latter is equivalent to a Wiener process subject to randomly
occurring jumps, whose probability law is obtained. The goodness of the
approximation is finally discussed.Comment: 18 pages, 5 figures, paper accepted by "Methodology and Computing in
Applied Probability", the final publication is available at
http://www.springerlink.co
Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics
The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α(t)x+β(t) and infinitesimal variance 2r(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
On the Absorbing Problems for Wiener, Ornstein–Uhlenbeck, and Feller Diffusion Processes: Similarities and Differences
For the Wiener, Ornstein–Uhlenbeck, and Feller processes, we study the transition probability density functions with an absorbing boundary in the zero state. Particular attention is paid to the proportional cases and to the time-homogeneous cases, by obtaining the first-passage time densities through the zero state. A detailed study of the asymptotic average of local time in the presence of an absorbing boundary is carried out for the time-homogeneous cases. Some relationships between the transition probability density functions in the presence of an absorbing boundary in the zero state and between the first-passage time densities through zero for Wiener, Ornstein–Uhlenbeck, and Feller processes are proven. Moreover, some asymptotic results between the first-passage time densities through zero state are derived. Various numerical computations are performed to illustrate the role played by parameters
- …