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Higher cumulants of conserved charges are sensitive observables of quantum chromodynamics phase transitions. The sample of mixed events provides a background to estimate non-critical effects of cumulants. Four possible methods for…
IIn this paper we provide predictable and chaotic representations for It\^{o}-Markov additive processes $X$. Such a process is governed by a finite-state CTMC $J$ which allows one to modify the parameters of the It\^{o}-jump process (in…
We generalize and extend the recently proposed method to account for contributions of system size (or volume/participant) fluctuations to the experimentally measured moments of particle multiplicity distributions. We find that in the…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…
An alternative parametric description for discrete random variables, called muculants, is proposed. In contrast to cumulants, muculants are based on the Fourier series expansion, rather than on the Taylor series expansion, of the logarithm…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
We determine that the sizes of bursts in mean-square current density in a reduced magnetohydrodynamic (RMHD)simulation follow power-law probability density function (PDF). The PDFs for burst durations and waiting time between bursts are…
Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set $B$ before another set $A$, and it is assumed that this probability satisfies a large…
Besides the classical motivation of fusing evidence from multiple sources, modern inferential procedures based on randomization, resampling, and data splitting often introduce analyst-generated multiplicity, where aggregating outputs across…
We compute the moment of order n of the Poisson stochastic integral of a random process u over a metric space X as a sum that runs over all partitions of {1,...,n} and involves the addition of points to Poisson configurations. This formula…
We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures,…
The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…
The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…
The paper deals with a mathematical model of a surveillance system based on a net of sensors. The signals acquired by each node of the net are Markovian process, have two different transition probabilities, which depends on the presence or…
Traditional methods for covariate adjustment of treatment means in designed experiments are inherently conditional on the observed covariate values. In order to develop a coherent general methodology for analysis of covariance, we propose a…
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…
Recent work has shown that the distribution of inter-event times for e-mail communication exhibits a heavy tail which is statistically consistent with a cascading Poisson process. In this work we extend the analysis to higher-order…
Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new…