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Stefan M. Moser - One of the best experts on this subject based on the ideXlab platform.
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The Fading Number of Multiple-Input Multiple-Output Fading Channels With Memory
IEEE Transactions on Information Theory, 2009Co-Authors: Stefan M. MoserAbstract:The fading number of a general (not necessarily Gaussian) regular multiple-input multiple-output (MIMO) fading channel with arbitrary temporal and spatial memory is derived. The channel is assumed to be noncoherent, i.e., neither receiver nor transmitter have knowledge about the channel state, but they only know the Probability Law of the fading process. The fading number is the second term in the asymptotic expansion of channel capacity when the signal-to-noise ratio (SNR) tends to infinity. It is related to the border of the high-SNR region with double-logarithmic capacity growth.
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the fading number of multiple input multiple output fading channels with memory
International Symposium on Information Theory, 2007Co-Authors: Stefan M. MoserAbstract:The fading number of a general (not necessarily Gaussian) regular multiple-input multiple-output (MIMO) fading channel with arbitrary temporal and spatial memory is derived. The channel is assumed to be non-coherent, i.e., neither receiver nor transmitter have knowledge about the channel state, but they only know the Probability Law of the fading process. The fading number is the second term in the asymptotic expansion of channel capacity when the signal-to-noise ratio (SNR) tends to infinity. It is shown that the fading number can be achieved by an input that is the product of two independent processes: a stationary and circularly symmetric direction- (or unit-) vector process whose distribution needs to be chosen such that it maximizes the fading number, and a non-negative magnitude process that is independent and identically distributed (IID) and that escapes to infinity. Additionally, in the more general context of an arbitrary stationary channel model satisfying some weak conditions on the channel Law, it is shown that the optimal input distribution is stationary apart from some edge effects.
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the fading number of simo fading channels with memory
2004Co-Authors: Amos Lapidoth, Stefan M. MoserAbstract:We derive the fading number of a general (not necessarily Gaussian) single-input multiple-output (SIMO) fading channel with memory, where the transmitter and receiver—while fully cognizant of the Probability Law governing the fading process—have no access to the fading realization. It is demonstrated that the fading number is achieved by IID circularly-symmetric inputs of log squared-magnitude that is uniformly distributed over a signal-to-noise (SNR) dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sub-logarithmically in the SNR. Among the new ingredients in the proof is a new theorem regarding input distributions that escape to infinity. Upper and lower bounds on the fading number for SIMO Gaussian fading are also presented. Those are computed explicitly for stationary m-th order autoregressive AR(m) Gaussian fading processes.
Antonio Di Crescenzo - One of the best experts on this subject based on the ideXlab platform.
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a new model of campi flegrei inflation and deflation episodes based on brownian motion driven by the telegraph process
Mathematical Geosciences, 2018Co-Authors: Fabio Travaglino, Antonio Di Crescenzo, Barbara Martinucci, R ScarpaAbstract:A stochastic model to describe the vertical motions in the Campi Flegrei volcanic region is proposed herein, consisting of a Brownian motion process driven by a generalized telegraph process. Knowledge on the Probability Law of this process enables quantitative investigation of some basic parameters regulating the inflation/deflation processes, such as velocities and time constants. Statistical analysis was carried out based on linear regression with constraints. Predictions of ground displacements and their changing tendency at future time instants were also made. Finally, a statistical test on the Brownian component of the process confirmed the goodness of the model.
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Probability Law and flow function of brownian motion driven by a generalized telegraph process
Methodology and Computing in Applied Probability, 2015Co-Authors: Antonio Di Crescenzo, Shelemyahu ZacksAbstract:We consider a standard Brownian motion whose drift alternates randomly between a positive and a negative value, according to a generalized telegraph process. We first investigate the distribution of the occupation time, i.e. the fraction of time when the motion moves with positive drift. This allows to obtain explicitly the Probability Law and the flow function of the random motion. We discuss three special cases when the times separating consecutive drift changes have (i) exponential distribution with constant rates, (ii) Erlang distribution, and (iii) exponential distribution with linear rates. In conclusion, in view of an application in environmental sciences we evaluate the density of a Wiener process with infinitesimal moments alternating at inverse Gaussian distributed random times.
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on the geometric brownian motion with alternating trend
2014Co-Authors: Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu ZacksAbstract:A basic model in mathematical finance theory is the celebrated geometric Brownian motion. Moreover, the geometric telegraph process is a simpler model to describe the alternating dynamics of the price of risky assets. In this note we consider a more general stochastic process that combines the characteristics of such two models. Precisely, we deal with a geometric Brownian motion with alternating trend. It is defined as the exponential of a standard Brownian motion whose drift alternates randomly between a positive and a negative value according to a generalized telegraph process. We express the Probability Law of this process as a suitable mixture of Gaussian densities, where the weighting measure is the Probability Law of the occupation time of the underlying telegraph process.
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a double ended queue with catastrophes and repairs and a jump diffusion approximation
Methodology and Computing in Applied Probability, 2012Co-Authors: Antonio Di Crescenzo, Virginia Giorno, Balasubramanian Krishna Kumar, Amelia Giuseppina NobileAbstract: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.
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On the damped geometric telegrapher’s process
'Springer Science and Business Media LLC', 2012Co-Authors: Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu ZacksAbstract:The geometric telegrapher's process has been proposed in 2002 as a model to describe the dynamics of the price of risky assets. In this contribution we consider a related stochastic process, whose trajectories have two alternating slopes, for which the random times between consecutive slope changes have exponential distribution with linearly increasing parameters. This leads to a process characterized by a damped behavior. We study the main features of the transient Probability Law of the process, and of its stationary limit
Barbara Martinucci - One of the best experts on this subject based on the ideXlab platform.
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a new model of campi flegrei inflation and deflation episodes based on brownian motion driven by the telegraph process
Mathematical Geosciences, 2018Co-Authors: Fabio Travaglino, Antonio Di Crescenzo, Barbara Martinucci, R ScarpaAbstract:A stochastic model to describe the vertical motions in the Campi Flegrei volcanic region is proposed herein, consisting of a Brownian motion process driven by a generalized telegraph process. Knowledge on the Probability Law of this process enables quantitative investigation of some basic parameters regulating the inflation/deflation processes, such as velocities and time constants. Statistical analysis was carried out based on linear regression with constraints. Predictions of ground displacements and their changing tendency at future time instants were also made. Finally, a statistical test on the Brownian component of the process confirmed the goodness of the model.
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on the geometric brownian motion with alternating trend
2014Co-Authors: Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu ZacksAbstract:A basic model in mathematical finance theory is the celebrated geometric Brownian motion. Moreover, the geometric telegraph process is a simpler model to describe the alternating dynamics of the price of risky assets. In this note we consider a more general stochastic process that combines the characteristics of such two models. Precisely, we deal with a geometric Brownian motion with alternating trend. It is defined as the exponential of a standard Brownian motion whose drift alternates randomly between a positive and a negative value according to a generalized telegraph process. We express the Probability Law of this process as a suitable mixture of Gaussian densities, where the weighting measure is the Probability Law of the occupation time of the underlying telegraph process.
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On the damped geometric telegrapher’s process
'Springer Science and Business Media LLC', 2012Co-Authors: Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu ZacksAbstract:The geometric telegrapher's process has been proposed in 2002 as a model to describe the dynamics of the price of risky assets. In this contribution we consider a related stochastic process, whose trajectories have two alternating slopes, for which the random times between consecutive slope changes have exponential distribution with linearly increasing parameters. This leads to a process characterized by a damped behavior. We study the main features of the transient Probability Law of the process, and of its stationary limit
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a damped telegraph random process with logistic stationary distribution
Journal of Applied Probability, 2010Co-Authors: Antonio Di Crescenzo, Barbara MartinucciAbstract:We introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the Probability Law of the motion, which admits a logistic stationary limit in a special case. Various results on the distributions of the maximum of the process and of the first passage time through a constant boundary are also given.
Shelemyahu Zacks - One of the best experts on this subject based on the ideXlab platform.
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Probability Law and flow function of brownian motion driven by a generalized telegraph process
Methodology and Computing in Applied Probability, 2015Co-Authors: Antonio Di Crescenzo, Shelemyahu ZacksAbstract:We consider a standard Brownian motion whose drift alternates randomly between a positive and a negative value, according to a generalized telegraph process. We first investigate the distribution of the occupation time, i.e. the fraction of time when the motion moves with positive drift. This allows to obtain explicitly the Probability Law and the flow function of the random motion. We discuss three special cases when the times separating consecutive drift changes have (i) exponential distribution with constant rates, (ii) Erlang distribution, and (iii) exponential distribution with linear rates. In conclusion, in view of an application in environmental sciences we evaluate the density of a Wiener process with infinitesimal moments alternating at inverse Gaussian distributed random times.
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on the geometric brownian motion with alternating trend
2014Co-Authors: Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu ZacksAbstract:A basic model in mathematical finance theory is the celebrated geometric Brownian motion. Moreover, the geometric telegraph process is a simpler model to describe the alternating dynamics of the price of risky assets. In this note we consider a more general stochastic process that combines the characteristics of such two models. Precisely, we deal with a geometric Brownian motion with alternating trend. It is defined as the exponential of a standard Brownian motion whose drift alternates randomly between a positive and a negative value according to a generalized telegraph process. We express the Probability Law of this process as a suitable mixture of Gaussian densities, where the weighting measure is the Probability Law of the occupation time of the underlying telegraph process.
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On the damped geometric telegrapher’s process
'Springer Science and Business Media LLC', 2012Co-Authors: Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu ZacksAbstract:The geometric telegrapher's process has been proposed in 2002 as a model to describe the dynamics of the price of risky assets. In this contribution we consider a related stochastic process, whose trajectories have two alternating slopes, for which the random times between consecutive slope changes have exponential distribution with linearly increasing parameters. This leads to a process characterized by a damped behavior. We study the main features of the transient Probability Law of the process, and of its stationary limit
Sylvia Fruhwirthschnatter - One of the best experts on this subject based on the ideXlab platform.
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markov chain monte carlo estimation of classical and dynamic switching and mixture models
Journal of the American Statistical Association, 2001Co-Authors: Sylvia FruhwirthschnatterAbstract:Bayesian estimation of a very general model class, where the distribution of the observations depends on a latent process taking values in a discrete state space, is discussed in this article. This model class covers finite mixture modeling, Markov switching autoregressive modeling, and dynamic linear models with switching. The consequences the unidentifiability of this type of model has on Markov chain Monte Carlo (MCMC) estimation are explicitly dealt with. Joint Bayesian estimation of all latent variables, model parameters, and parameters that determine the Probability Law of the latent process is carried out by a new MCMC method called permutation sampling. The permutation sampler first samples from the unconstrained posterior–which often can be done in a convenient multimove manner–and then applies a permutation of the current labeling of the states of the latent process. In a first run, the random permutation sampler used selected the permutation randomly. The MCMC output of the random permutation s...