Related papers: Selfdecomposability, perpetuity and stopping times
The transformation of canonical decay laws of moving unstable quantum systems is studied by approximating, over intermediate times, the decay laws at rest with superpositions of exponential modes via the Prony analysis. The survival…
Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
An essential character for a distribution to play a central role in the limit theory is infinite divisibility. In this note, we prove that the Conway-Maxwell-Poisson (CMP) distribution is infinitely divisible iff it is the Poisson or…
We define {\em predictive information} $I_{\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\rm…
We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated L\'evy walks observed in active intracellular transport by…
Let $\boxplus$, $\boxtimes$ and $\uplus$ be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure $\mu$ on $[0,\infty)$ with finite second moment, we find the scaling limit of…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…
In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do…
We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…
Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…
We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed…
The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the L\'evy stable distributions, and more…
For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n}…
We consider the set of finite sequences of length n over a finite or countable alphabet C. We consider the function which associate each given sequence with the size of the maximum overlap with a (shifted) copy of itself. We compute the…
Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The…
The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…
The relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (non-vanishing) lower bound $\mu_0$ of the mass spectrum. The survival…
The law of a positive infinitely divisible process with no drift is characterized by its L\'evy measure on the paths space. Based on recent results of the two authors, it is shown that even for simple examples of such processes, the…