Search results for " function"
showing 10 items of 9395 documents
Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model
2016
We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients on a state space with certain boundary conditions. The drift depends on time and space and is periodic in the time argument. There is no time dependence in the diffusion coefficient. Control systems play a key role, and we prove a new localized version of the support theorem. Beyond existence of some Lyapunov function, we only need one attainable inner point of full weak Hoermander dimension. Our motivation comes from a stochastic Hodgkin−Huxley model for a spiking neuron including its dendritic input. This input carries some deterministic periodic si…
Stability of a stochastic SIR system
2005
Abstract We propose a stochastic SIR model with or without distributed time delay and we study the stability of disease-free equilibrium. The numerical simulation of the stochastic SIR model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found.
Assessing covariate imbalance in meta-analysis studies.
2010
The main goal of meta-analysis is to combine data across studies or data sets to obtain summary estimates. In this paper, the novelty is to propose a statistical tool to assess a possible covariate imbalance in baseline variables to investigate similarity of trials. We conducted the detection of the covariate imbalance, first, through some graphical comparison of the empirical cumulative distribution functions or ECDFs, which are built by putting together arms or trials according to some risk factor, and second, through some non-parametric tests such as the Kolmogorov–Smirnov and the Anderson–Darling tests. To overcome the huge presence of ties, we conducted the statistical tests on perturbe…
Lyapunov exponent and topological entropy plateaus in piecewise linear maps
2013
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.
Fractal eigenstates in disordered systems
1990
Abstract The wave functions of the non-interacting electrons in disordered systems described by a tight-binding model with site-diagonal disorder are investigated by means of the inverse participation ratio. The wave functions are shown to be fractal objects. In three-dimensional samples, a critical fractal dimension can be defined for the mobility edge in the band centre, which yields the mobility edge trajectory in the whole energy range in good agreement with previous calculations based on the investigation of the exponentially decaying transmission coefficient.
Statistics of return times for weighted maps of the interval
2000
For non markovian, piecewise monotonic maps of the interval associated to a potential, we prove that the law of the entrance time in a cylinder, when renormalized by the measure of the cylinder, converges to an exponential law for almost all cylinders. Thanks to this result, we prove that the fluctuations of Rn, first return time in a cylinder, are lognormal.
Elasticity function of a discrete random variable and its properties
2017
ABSTRACTElasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavia (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuou…
Exponential and bayesian conjugate families: Review and extensions
1997
The notion of a conjugate family of distributions plays a very important role in the Bayesian approach to parametric inference. One of the main features of such a family is that it is closed under sampling, but a conjugate family often provides prior distributions which are tractable in various other respects. This paper is concerned with the properties of conjugate families for exponential family models. Special attention is given to the class of natural exponential families having a quadratic variance function, for which the theory is particularly fruitful. Several classes of conjugate families have been considered in the literature and here we describe some of their most interesting feat…
SPECTRAL ANALYSIS WITH TAPERED DATA
1983
. A new method based on an upper bound for spectral windows is presented for investigating the cumulants of time series statistics. Using this method two classical results are proved for tapered data. In particular, the asymptotic normality for a class of spectral estimates including estimates for the spectral function and the covariance function is proved under integrability conditions on the spectra using the method of cumulants.
Model comparison and selection for stationary space–time models
2007
An intensive simulation study to compare the spatio-temporal prediction performances among various space-time models is presented. The models having separable spatio-temporal covariance functions and nonseparable ones, under various scenarios, are also considered. The computational performance among the various selected models are compared. The issue of how to select an appropriate space-time model by accounting for the tradeoff between goodness-of-fit and model complexity is addressed. Performances of the two commonly used model-selection criteria, Akaike information criterion and Bayesian information criterion are examined. Furthermore, a practical application based on the statistical ana…