Related papers: Functional statistical inference of parton distrib…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
We investigate the feasibility of constraining parton distribution functions in the proton through a comparison with data on semi-inclusive deep-inelastic lepton-nucleon scattering. Specifically, we reweight replicas of these distributions…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
A new generation of (unpolarized) dynamical parton distribution functions of the nucleon is determined. After introducing basic elements of perturbative QCD, the dynamical model is discussed and compared with the approach to parton…
In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent…
The theoretical foundations of the quantum statistical approach to parton distributions are reviewed together with the phenomenological motivations from a few specific features of Deep Inelastic Scattering data. The chiral properties of QCD…
Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
We consider the generic problem of performing a global fit to many independent data sets each with a different overall multiplicative normalization uncertainty. We show that the methods in common use to treat multiplicative uncertainties…
A new fractional non-homogeneous counting process has been introduced and developed using the Kilbas and Saigo three-parameter generalization of the Mittag-Leffler function. The probability distribution function of this process reproduces…
We introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define…
We remark that the often ignored quantum probability current is fundamental for a genuine understanding of scattering phenomena and, in particular, for the statistics of the time and position of the first exit of a quantum particle from a…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
We explore some probabilistic applications arising in connections with $K$-theoretic symmetric functions. For instance, we determine certain corner distributions of random lozenge tilings and plane partitions. We also introduce some…
We characterise probability distributions via a martingale property associated with a natural generalisation of record values, known as $\delta$-records. For an independent and identically distributed sequence $(X_n)$ with running maximum…
We present a fit to spin asymmetries which gives polarized quark distributions. These functions are closely related to the ones given by the newest Martin, Roberts and Stirling fit for unpolarized structure functions. The integrals of…