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395 results on '"Nobile, A. G."'

1. A continuous-time Ehrenfest model with catastrophes and its jump-diffusion approximation

Author

Dharmaraja, Selvamuthu, Di Crescenzo, Antonio, Giorno, Virginia, and Nobile, Amelia G.

Subjects
Mathematics - Probability, 60J80, 60J27, 60J60
Abstract

We consider a continuous-time Ehrenfest model defined over the integers from -N to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe instantaneously resets the process to state 0. We investigate both the transient and steady-state probabilities of the above model. Further, the first passage time through state 0 is discussed. We perform a jump-diffusion approximation of the above model, which leads to the Ornstein-Uhlenbeck process with catastrophes. The underlying jump-diffusion process is finally studied, with special attention to the symmetric case arising when the Ehrenfest model has equal upward and downward transition rates., Comment: 21 pages, 10 figures

Published
2021
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2. M/M/1 queue in two alternating environments and its heavy traffic approximation

Author

Di Crescenzo, Antonio, Giorno, Virginia, Kumar, Balasubramanian Krishna, and Nobile, Amelia G.

Subjects
Mathematics - Probability, 60K25, 60K37, 60J60, 60J70
Abstract

We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of the process in terms of a generalized mixture of two geometric distributions. In the special case when only one kind of switch is allowed, we analyze the transient distribution, and investigate the busy period problem. The analysis is also performed by means of a suitable heavy-traffic approximation which leads to a continuous random process. Its distribution satisfies a partial differential equation with randomly alternating infinitesimal moments. For the approximating process we determine the steady-state distribution, the transient distribution and a first-passage-time density., Comment: 31 pages, 18 figures

Published
2021
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5. Continuous-Time Birth-Death Chains Generate by the Composition Method

Author

Giorno, Virginia, Nobile, Amelia G., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Moreno-Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada-Arencibia, Alexis, editor

Published
2020
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6. Some Remarks on the Prendiville Model in the Presence of Jumps

Author

Giorno, Virginia, Nobile, Amelia G., Spina, Serena, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Moreno-Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada-Arencibia, Alexis, editor

Published
2020
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9. A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation

Author

Di Crescenzo, Antonio, Giorno, Virginia, Kumar, Balasubramanian Krishna, and Nobile, Amelia G.

Subjects
Mathematics - Probability, 60J80, 60J25
Abstract

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.com

Published
2011
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10. A Random Tandem Network with Queues Modeled as Birth-Death Processes

Author

Giorno, Virginia, Nobile, Amelia G., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Moreno-Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada-Arencibia, Alexis, editor

Published
2018
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12. Simulations of Gaussian Processes and Neuronal Modeling

Author

Di Nardo, Elvira, Nobile, Amelia G., Pirozzi, Enrica, and Ricciardi, Luigi M.

Subjects
Mathematics - Statistics Theory, 60G15, 60G10, 65C50
Abstract

The research work outlined in the present note highlights the essential role played by the simulation procedures implemented by us on CINECA supercomputers to complement the mathematical investigations carried within our group over the past several years. The ultimate target of our research is the understanding of certain crucial features of the information processing and transmission by single neurons embedded in complex networks. More specifically, here we provide a bird's eye look of some analytical, numerical and simulation results on the asymptotic behavior of first passage time densities for Gaussian processes, both of a Markov and of a non-Markov type. Several figures indicate significant similarities or diversities between computational and simulated results., Comment: Extended version of the paper published in Science and Supercomputing at CINECA - Report 2003 (Garofalo F., Moretti M., Voli M., eds.), 375-381. ISBN 88-86037-13-9

Published
2004

13. On the first-visit-time problem for birth and death processes with catastrophes

Author

Di Crescenzo, A., Giorno, V., Nobile, A. G., and Ricciardi, L. M.

Subjects
Mathematics - Probability, 60J27, 60J80
Abstract

For a birth-death process subject to catastrophes, defined on the state-space $S=\{r,r+1,r+2,...\}$, with $r$ a positive integer or zero, the first-visit time to a state $k\in S$ is considered and the Laplace transform of its probability density function is determined, use of which is then made to obtain mean and variance. The Laplace transform of the probability density function of the first effective catastrophe occurrence time and its expected value are also obtained. Some extensions to time-non-homogeneous processes are then provided. Finally, certain additional results concerning the determination of the steady-state distribution and the representation of the transition probabilities are worked out, while some applications to particular birth-death processes are shown in the Appendix., Comment: 23 pages, no figures

Published
2003

14. Towards the Modeling of Neuronal Firing by Gaussian Processes

Author

Di Nardo, E., Nobile, A. G., Pirozzi, E., and Ricciardi, L. M.

Subjects
Mathematics - Probability, Quantitative Biology, 60G15, 60G10, 92C20, 68U20, 65C50
Abstract

This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct histograms estimating the firing densities. Our results originate from the study of non-Markov stationary Gaussian neuronal models with the aim to determine the neuron's firing probability density function. A parallel algorithm has been implemented in order to simulate large numbers of sample paths of Gaussian processes characterized by damped oscillatory covariances in the presence of time dependent boundaries. The analysis based on the simulation procedure provides an alternative research tool when closed-form results or analytic evaluation of the neuronal firing densities are not available., Comment: 10 pages, 3 figures, to be published in Scientiae Mathematicae Japonicae

Published
2003

15. On the asymptotic behavior of first passage time densities for stationary Gaussian processes

Author

Di Nardo, E., Nobile, A. G., Pirozzi, E., and Ricciardi, L. M.

Subjects
Mathematics - Probability, 60G15, 60G10, 60G40
Abstract

Making use of a Rice-like series expansion, for a class of stationary Gaussian processes the asymptotic behavior of the first passage time probability density function through certain time-varying boundaries, including periodic boundaries, is determined. Sufficient conditions are then given such that the density asymptotically exhibits an exponential behavior when the boundary is either asymptotically constant or asymptotically periodic., Comment: 21 pages, 7 figures, to be published in Methodology and Computing in Applied Probability

Published
2003

24. On Time Non-homogeneous Feller-Type Diffusion Process in Neuronal Modeling

Author

Nobile, Amelia G., Pirozzi, Enrica, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Moreno-Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada-Arencibia, Alexis, editor

Published
2015
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25. Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models.

Author

Giorno, Virginia and Nobile, Amelia G.

Subjects
*EPIDEMICS, *STOCHASTIC models, *DISTRIBUTION (Probability theory)
Abstract

We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes, we determine the explicit expressions of the transition probabilities and of the first-passage time densities. For time-homogeneous finite birth processes, the behavior of the mean and the variance of the first-passage time density is also analyzed. Moreover, the approximate duration until the entire population is infected is obtained for a large population size. [ABSTRACT FROM AUTHOR]

Published
2023
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26. On a Bilateral Linear Birth and Death Process in the Presence of Catastrophes

Author

Giorno, Virginia, Nobile, Amelia G., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Moreno-Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada-Arencibia, Alexis, editor

Published
2013
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27. On the Construction of Densities for Time Non-homogeneous Diffusion Processes

Author

Giorno, Virginia, Nobile, Amelia G., Ricciardi, Luigi M., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Moreno-Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada-Arencibia, Alexis, editor

Published
2012
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30. Diffusion Processes Subject to Catastrophes

Author

di Cesare, Roberta, Giorno, Virginia, Nobile, Amelia G., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Moreno-Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada-Arencibia, Alexis, editor

Published
2009
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32. On the Estimation of First-Passage Time Densities for a Class of Gauss-Markov Processes

Author

Nobile, A. G., Pirozzi, E., Ricciardi, L. M., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Moreno Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada Arencibia, Alexis, editor

Published
2007
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36. Upcrossing First Passage Times for Correlated Gaussian Processes

Author

Giorno, Virginia, Nobile, Amelia G., Pirozzi, Enrica, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Moreno Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada Arencibia, Alexis, editor

Published
2005
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37. A Wiener Neuronal Model with Refractoriness

Author

Giorno, Virginia, Nobile, Amelia G., Ricciardi, Luigi M., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Moreno Díaz, Roberto, editor, Pichler, Franz, editor, and Quesada Arencibia, Alexis, editor

Published
2005
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38. Gaussian Processes and Neuronal Modeling

Author

Di Nardo, Elvira, Nobile, Amelia G., Pirozzi, Enrica, Ricciardi, Luigi M., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Mira, José, editor, and Álvarez, José R., editor

Published
2005
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39. On the Moments of Firing Numbers in Diffusion Neuronal Models with Refractoriness

Author

Giorno, Virginia, Nobile, Amelia G., Ricciardi, Luigi M., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Mira, José, editor, and Álvarez, José R., editor

Published
2005
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48. On the Absorbing Problems for Wiener, Ornstein–Uhlenbeck, and Feller Diffusion Processes: Similarities and Differences.

Author

Giorno, Virginia and Nobile, Amelia G.

Subjects
*PROBABILITY density function, *ORNSTEIN-Uhlenbeck process
Abstract

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. [ABSTRACT FROM AUTHOR]

Published
2023
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