Related papers: A Note on Uniform Integrability of Random Variable…
In the classical probability in continuous random variables there is no distinguishing between the probability involving strict inequality and non strict inequality. Moreover a probability involves equality collapse to zero without…
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…
It is proved that in suitable filtrations every pair of integrable random variables is the conditional expectation of a pair of commonotone integrable random variables.
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the…
Probability integral transforms (PITs) and empirical $p$-values are widely used to assess the calibration of predictive distributions. While exact PIT values are uniformly distributed under correct model specification, practical…
A recent line of work provides new statistical tools based on game-theory and achieves safe anytime-valid inference without assuming regularity conditions. In particular, the framework of universal inference proposed by Wasserman, Ramdas…
In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational…
The main purpose of this paper is to introduce a new sequence space by using de la Vallee-Poussin mean and investigate both the modular structure with some geometric properties and some topological properties with respect to the Luxemburg…
It is shown that at least 50% of the probability mass of a sum of independent Rademacher random variables is within one standard deviation from its mean. This lower bound is sharp, it is much better than for instance the bound that can be…
We elaborate the notions of Martin-L\"of and Schnorr randomness for real numbers in terms of uniform distribution of sequences. We give a necessary condition for a real number to be Schnorr random expressed in terms of classical uniform…
We propose a criterion of equidistribution by the differentiability of certain arithmetic invariants. Combined with the slope method and the asymptotic measures, this criterion gives a new "conceptual" proof to equidistribution results…
In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result…
Given a submodular capacity space, we prove the uniform convergence in capacity and also the uniform convergence in the Choquet-mean of order $p\ge1$ with a quantitative estimate, of the multivariate Bernstein polynomials associated to a…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
Consider $n$ independent random numbers with a uniform distribution on $[0,1]$. The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is described by the Eulerian numbers. This is related to, but…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…