Related papers: Evolution equations of the probabilistic generaliz…
In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of…
We present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous many-particle system in terms of…
The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative…
We investigate the upscaling of diffusive transport parameters as function of pore scale material structure using a stochastic framework. We focus on sub-REV (representative elementary volume) scale where the complexity of pore space…
The recently developed Wigner functional theory is used to formulate an evolution equation for arbitrary multi-photon states, propagating through a turbulent atmosphere under arbitrary conditions. The resulting evolution equation, which is…
We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…
The infinitely-many-neutral-alleles model has recently been extended to a class of diffusion processes associated with Gibbs partitions of two-parameter Poisson-Dirichlet type. This paper introduces a family of infinite-dimensional…
The evolution operator method is used to solve the generalized Fokker-Planck equations and the generalized diffusion-wave equations in the (1+1) dimensional space in which $x\in\mathbb{R}$ and $t\in\mathbb{R}_+$. These equations contain…
When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
According to modern developments in turbulence theory, the "dissipation" scales (u.v. cut-offs) $\eta$ form a random field related to velocity increments $\delta_{\eta}u$. In this work we, using Mellin's transform combined with the Gaussain…
This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson…
We study statistical properties of galaxy structures in several samples extracted from the 2dF Galaxy Redshift Survey. In particular, we measured conditional fluctuations by means of the scale-length method and determined their probability…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
In ref [math.ST/0411462] the notion of statistically dual distributions is introduced. The reconstruction of confidence density [AIP Conference Proceedings 803 (2005) 398] for the location parameter for several pairs of statistically dual…