1,721,106 research outputs found
Some remarks on stochastic diffusion processes with jumps
No full textWe consider stochastic diffusion processes subject to jumps that occur at
random times. We assume that after each jump the process is reset to a random state from
which it can evolve with a different dynamics. For this kind of processes the transition
probability density function and its moments are analyzed. Moreover, the first passage
time problem is studied. The results are applied to the processes with jumps constructed
on the Wiener diffusion process
A rumor spreading model with random denials
No full textThe concept of denial is introduced on rumor spreading processes. The denials occur with a certain rate and they reset to start the initial situation. A population of N individuals is subdivided into ignorants, spreaders and stiflers; at the initial time there is only one spreader and the rest of the population is ignorant. The denials are introduced in the classic DK model and in its generalization, in which a spreader can transmit the rumor at most to k ignorants. The steady state densities are analyzed for these models. Finally, a numerical analysis is performed to study the rule of the involved parameters and to compare the proposed models
A Stochastic model in Tumor Growth
No full textA stochastic model of solid tumor growth based on deterministic Gompertz law is presented. Tumor cells evolution is described by a
one-dimensional diffusion process limited by two absorbing boundaries representing healing threshold and patient death (carrying
capacity), respectively. Via a numerical approach the first exit time problem is analysed for the process inside the region restricted by the
boundaries. The proposed model is also implemented to simulate the effects of a time-dependent therapy. Finally, some numerical results
are obtained for the specific case of a parathyroid tumor
On the return process with refractoriness for non-homogeneous Ornstein-Uhlenbeck neuronal model
No full textAn Ornstein-Uhlenbeck diffusion process is considered as a model
for the membrane potential activity of a single neuron. We assume that the
neuron is subject to a sequence of inhibitory and excitatory post-synaptic potentials that occur with time-dependent rates. The resulting process is characterized by time-dependent drift. For this model, we construct the return
process describing the membrane potential. It is a non homogeneous Ornstein-
Uhlenbeck process with jumps on which the effect of random refractoriness
is introduced. An asymptotic analysis of the process modeling the number
of firings and the distribution of interspike intervals is performed under the
assumption of exponential distribution for the firing time. Some numerical
evaluations are performed to provide quantitative information on the role of
the parameters
Towards a two-compartment model in tumor growth
No full textA stochastic model of tumor growth incorporating several key elements
of the growth processes is presented. Generalizing a previous work by the authors,
two one-dimensional diffusion processes representing populations of proliferating and
quiescent cells are obtained. Their forms turn out by their relation with total tumor
population analysed in [1]. The proposed model is able to incorporate the effects of the
mutual interactions between the two subpopulations. It is also used to simulate the
effects of two kinds of time-dependent therapies: non-specific cycle and specific cycle
drugs. Moreover, the first-exit-time problem is analyzed to study cancer evolution in
the presence of a time-dependent therapy
On the return process with refractoriness for non-homogeneous Ornstein-Uhlenbeck neuronal model
No full textInference on the effect of non homogeneous inputs in Ornstein-Uhlenbeck neuronal modeling
Full text linkA non-homogeneous Ornstein-Uhlembeck (OU) diffusion process is considered as a model for the membrane potential activity of a single neuron. We assume that, in the absence of stimuli, the neuron activity is described via a time-homogeneous process with linear drift and constant infinitesimal variance. When a sequence of inhibitory and excitatory post-synaptic potentials occurres with generally time-dependent rates, the membrane potential is then modeled by means of a non-homogeneous OU-type process. From a biological point of view it becomes important to understand the behavior of the membrane potential in the presence of such stimuli. This issue means, from a statistical point of view, to make inference on the resulting process modeling the phenomenon. To this aim, we derive some probabilistic properties of a non-homogeneous OU-type process and we provide a statistical procedure to fit the constant parameters and the time-dependent functions involved in the model. The proposed methodology is based on two steps: the first one is able to estimate the constant parameters, while the second one fits the non-homogeneous terms of the process. Related to the second step two methods are considered. Some numerical evaluations based on simulation studies are performed to validate and to compare the proposed procedures
On the distribution of the range of an asymmetric random walk
No full textWe provide an alternative procedure for determining the range distribution, whose virtue is its much greater simplicity and effectiveness for computational purposes. Indeed,
our closed-form results are deprived of the rapidly oscillating trigonometric terms. The well-known convergence of a r.w. to a Wiener process is finally exploited to obtain an asymptotic formula for the mean range of the r.w
Time-Inhomogeneous Feller-type Diffusion Process with Absorbing Boundary Condition
No full textA 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
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