Related papers: Measures of Variance on Windowed Gaussian Processe…
Aperiodic variability is a characteristic feature of young stars, massive stars, and active galactic nuclei. With the recent proliferation of time domain surveys, it is increasingly essential to develop methods to quantify and analyze…
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and…
We determine the variance for the fluctuations of the arithmetic measures obtained by collecting all closed geodesics on the modular surface with the same discriminant and ordering them by the latter. This arithmetic variance differs by…
We analyze different data of the variation of the fine structure constant obtained with different methods to check their consistency.We test consistency using the modified Student test and confidence intervals. We split the data sets in…
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We…
In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are…
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…
As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterise and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources,…
In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown…
Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
We introduce a new approach for Gaussianity testing using the envelope of a signal and its coefficient of variation. The envelope of a Gaussian signal follows the Rayleigh distribution, and given that the coefficient of variation of the…
Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…
We obtained a semi-analytical treatment obtaining estimators for the sample variance and variance of sample variance for the RTS noise. Our method suggests a way to experimentally determine the constants of capture and emission in the case…
A class of Gaussian processes generalizing the usual fractional Brownian motion for Hurst indices in (1/2,1) and multifractal Brownian motion introduced in Ralchenko and Shevchenko (Theory Probab Math Stat 80, 2010) and Boufoussi et al.…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…