相关论文: Measures of Variance on Windowed Gaussian Processe…

We consider a smooth, rotationally invariant, centered gaussian process in the plane, with arbitrary correlation matrix $C_{t t'}$. We study the winding angle $\phi_t$ around its center. We obtain a closed formula for the variance of the…

It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…

We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the winding number as the time horizon tends to infinity.…

Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly,…

The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…

The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with…

Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…

The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic…

Mode splittings produced by uniform rotation and a particular form of differential rotation are computed for two-dimensional rotating 10 Mo ZAMS stellar models. The change in the character of the mode splitting is traced as a function of…

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…

In the analysis of variable stars, the problem of sampling is central. This article focusses on the determination of the Nyquist frequency. It is well defined in the case of regular sampling. However, the time series of variable stars…

We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random…

Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian…

Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…

Many astrophysical phenomena are time-varying, in the sense that their brightness change over time. In the case of periodic stars, previous approaches assumed that changes in period, amplitude, and phase are well described by either…

A common approach to model memristive systems is to include empirical window functions to describe edge effects and non-linearities in the change of the memristance. We demonstrate that under quite general conditions, each window function…

Measurements of the spectrum of the fluctuations of the output current of the quadratic detector of a telescope can be used to find unresolved astronomical gravitational lenses and determine time delays between their image components. These…

We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…

It is demonstrated that in low multiplicity sample, the increase of the fluctuation of event-factorial-moments with the diminishing of phase space scale, called ``erraticity'', are dominated by the statistical fluctuations. The erraticity…