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

The stochastic calculus for Gaussian processes is applied to obtain a Tanaka formula for a Volterra-type multifractional Gaussian process. The existence and regularity properties of the local time of this process are obtained by means of…

The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar…

We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…

The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability density for its position coordinate, which makes it suitable…

The Interstellar Medium (ISM) is a complex, multi-phase system, where the history of the stars occurs. The processes of birth and death of stars are strongly coupled to the dynamics of the ISM. The observed chaotic and diffusive motions of…

In a recent paper, published at arXiv:0910.2381, we started a discussion on the new possibilities arising from the use of fractional differential calculus in image processing. We have seen that the fractional calculation is able to enhance…

In this paper we introduce a definition of a multi-dimensional fractional Brownian motion of Hurst index $H \in (0, 1)$ under volatility uncertainty (in short G-fBm). We study the properties of such a process and provide first results about…

We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…

Clumping in stellar winds of hot stars is a possible consequence of radiative-acoustic instability appearing in solutions of radiative-hydrodynamical equations. However, clumping is usually included to stellar atmosphere modeling and…

When a gravitational wave (GW) from a distant source propagates through the universe, its amplitude and phase change due to gravitational lensing by the inhomogeneous mass distribution. We derive the amplitude and phase fluctuations, and…

We present the first framework for Gaussian-process-modulated Poisson processes when the temporal data appear in the form of panel counts. Panel count data frequently arise when experimental subjects are observed only at discrete time…

In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than…

Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…

We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the…

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…

Using very long baseline interferometry data for the sources that comprise the third International Celestial Reference Frame (ICRF3), we examine the quality of the formal source position uncertainties of ICRF3 by determining the excess…

Single-point measurements of fluctuations in the scrape-off layer of magnetized plasmas are generally found to be dominated by large-amplitude bursts which are associated with radial motion of blob-like structures. A stochastic model for…

Gamma ray burst (GRB) time series is a non-stationary time series with all its statistical properties varying with time. Considering that each GRB is a different manifestation of the same stochastic process we studied the time dependent as…

In this note we present the starry_process code, which implements an interpretable Gaussian process (GP) for modeling variability in stellar light curves. As dark starspots rotate in and out of view, the total flux received from a distant…

Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…