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We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
We consider smoothing equations of the form $$X ~\stackrel{\mathrm{law}}{=}~ \sum_{j \geq 1} T_j X_j + C$$ where $(C,T_1,T_2,\ldots)$ is a given sequence of random variables and $X_1,X_2,\ldots$ are independent copies of $X$ and independent…
The univariate distorted distribution were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks. Later they were also applied to represent distributions of order statistics, coherent…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
We study finite probability theory through a category of finite probability schemes and probability-preserving maps, called \emph{bundles}. A bundle simultaneously records a quotient of a sample space, an algebra of random variables, and…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representation of quantum mechanics. Example of entangled probability…
This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
Characterizations of finite sequences $\beta_{1}<\cdots<\beta_{n}$ representing expected values of order statistics from a random sample of size $n$ are given. As a by-product, a characterization of binomial mixtures, when the mixing random…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
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…