Stochastic ordering of random processes with an imbedded point process

1991 ◽  
Vol 28 (3) ◽  
pp. 553-567 ◽  
Author(s):  
François Baccelli
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Random Sequence ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Time Process ◽  
Continuous Time Process ◽  
Partial Orderings ◽  
Stationary Probabilities

We introduce multivariate partial orderings related with the Palm and time-stationary probabilities of a point process. Using these orderings, we give conditions for the monotonicity of a random sequence, with respect to some integral stochastic ordering, to be inherited with a continuous time process in which this sequence is imbedded. This type of inheritance is also discussed for the property of association.

Stochastic ordering of random processes with an imbedded point process

1991 ◽  
Vol 28 (03) ◽  
pp. 553-567 ◽  
Author(s):  
François Baccelli
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Random Sequence ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Time Process ◽  
Continuous Time Process ◽  
Partial Orderings ◽  
Stationary Probabilities

We introduce multivariate partial orderings related with the Palm and time-stationary probabilities of a point process. Using these orderings, we give conditions for the monotonicity of a random sequence, with respect to some integral stochastic ordering, to be inherited with a continuous time process in which this sequence is imbedded. This type of inheritance is also discussed for the property of association.

COUPLING INTERACTING PARTICLE SYSTEMS

1993 ◽  
Vol 05 (03) ◽  
pp. 457-475 ◽  
Author(s):  
CHRISTIAN MAES
Keyword(s):  
Convergence Rate ◽  
Discrete Time ◽  
Continuous Time ◽  
Interacting Particle Systems ◽  
Random Processes ◽  
Particle Systems ◽  
Time Process ◽  
Probabilistic Cellular Automata ◽  
Interacting Particle ◽  
Continuous Time Process

We consider random processes (probabilistic cellular automata or interacting particle systems) defined through the interaction of an infinite number of components. We show how coupling arguments yield simple yet quite general ergodicity theorems. The relation between discrete time and continuous time versions is analyzed via similar techniques and the explicit convergence rate of discrete time approximations to the continuous time process is obtained.

STIT tessellations are Bernoulli and standard

2012 ◽  
Vol 34 (3) ◽  
pp. 876-892 ◽  
Author(s):  
SERVET MARTÍNEZ
Keyword(s):  
Continuous Time ◽  
Bernoulli Shift ◽  
Random Sequence ◽  
Time Process ◽  
Continuous Time Process ◽  
Stit Tessellation ◽  
Bernoulli Flow

AbstractLet (Yt:t>0) be a STIT tessellation process and a>1. We prove that the random sequence (anYan:n∈ℤ) is a non-anticipating factor of a Bernoulli shift. We deduce that the continuous time process (atYat:t∈ℝ) is a Bernoulli flow. We use the techniques and results in Martínez and Nagel [Ergodic description of STIT tessellations. Stochastics 84(1) (2012), 113–134]. We also show that the filtration associated to the non-anticipating factor is standard in Vershik’s sense.

scholarly journals Mixed Spectra for Stable Signals from Discrete Observations

2021 ◽  
Vol 12 (05) ◽  
pp. 21-44
Author(s):  
Rachid Sabre
Keyword(s):  
Spectral Density ◽  
Continuous Time ◽  
Continuous Measurement ◽  
Spectral Measurement ◽  
Polynomial Kernel ◽  
Time Process ◽  
Discrete Observations ◽  
Continuous Part ◽  
Continuous Time Process ◽  
Discrete Measurement

This paper concerns the continuous-time stable alpha symmetric processes which are inivitable in the modeling of certain signals with indefinitely increasing variance. Particularly the case where the spectral measurement is mixed: sum of a continuous measurement and a discrete measurement. Our goal is to estimate the spectral density of the continuous part by observing the signal in a discrete way. For that, we propose a method which consists in sampling the signal at periodic instants. We use Jackson's polynomial kernel to build a periodogram which we then smooth by two spectral windows taking into account the width of the interval where the spectral density is non-zero. Thus, we bypass the phenomenon of aliasing often encountered in the case of estimation from discrete observations of a continuous time process.

scholarly journals Likelihood Methods for Point Processes with Refractoriness

2014 ◽  
Vol 26 (2) ◽  
pp. 237-263 ◽  
Author(s):  
Luca Citi ◽  
Demba Ba ◽  
Emery N. Brown ◽  
Riccardo Barbieri
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Process Model ◽  
Point Processes ◽  
Linear Models ◽  
Continuous Time Model ◽  
Time Model ◽  
Fitting Procedures ◽  
Continuous Time Process ◽  
Conditional Intensity Function

Likelihood-based encoding models founded on point processes have received significant attention in the literature because of their ability to reveal the information encoded by spiking neural populations. We propose an approximation to the likelihood of a point-process model of neurons that holds under assumptions about the continuous time process that are physiologically reasonable for neural spike trains: the presence of a refractory period, the predictability of the conditional intensity function, and its integrability. These are properties that apply to a large class of point processes arising in applications other than neuroscience. The proposed approach has several advantages over conventional ones. In particular, one can use standard fitting procedures for generalized linear models based on iteratively reweighted least squares while improving the accuracy of the approximation to the likelihood and reducing bias in the estimation of the parameters of the underlying continuous-time model. As a result, the proposed approach can use a larger bin size to achieve the same accuracy as conventional approaches would with a smaller bin size. This is particularly important when analyzing neural data with high mean and instantaneous firing rates. We demonstrate these claims on simulated and real neural spiking activity. By allowing a substantive increase in the required bin size, our algorithm has the potential to lower the barrier to the use of point-process methods in an increasing number of applications.

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