Related papers: A Note on Uniform Integrability of Random Variable…

In a recent paper \cite{CHR16}, Chandra, Hu and Rosalsky introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. In this note, we…

In this paper, we explore an abstraction of uniform integrability in vector lattices and demonstrate its application by providing a positive solution to an open question posed by Kuo, Rodda, and Watson. Specifically, we show that for finite…

In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…

This note establishes convergence in mean of order $p$, $0<p\le 1$ for $d$-dimensional arrays of random vectors in Hilbert spaces under the Ces\`{a}ro uniform integrability conditions. In the case where $0<p<1$, our $L_p$ convergence is…

We consider several general conditions for integrability of two Roumieu ultradistributions and prove their equivalence. The discussed sequential conditions are based on two classes of approximate units and allow one to introduce sequential…

The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…

In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…

We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…

Let $L^0$ be the vector space of all (equivalence classes of) real-valued random variables built over a probability space $(\Omega, \mathcal{F}, P)$, equipped with a metric topology compatible with convergence in probability. In this work,…

Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…

In ref [math.ST/0411462] the notion of statistically dual distributions is introduced. The reconstruction of confidence density [AIP Conference Proceedings 803 (2005) 398] for the location parameter for several pairs of statistically dual…

We introduce and investigate in this paper a new convenient method of introduction of a norm in the multidimensional rearrangement probability invariant space.

For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to…

We present a simple solution to a question posed by Candes, Romberg and Tao on the uniform uncertainty principle for Bernoulli random matrices. More precisely, we show that a rectangular k*n random subgaussian matrix (with k < n) has the…

We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…

As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…

We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established in [E. Mossel, R. O'Donnell and K. Oleszkiewicz (2010). Noise stability of functions with low…

Two classes of topological spaces are introduced on which every probability Radon measure possesses a uniformly distributed sequence or a uniformly tight uniformly distributed sequence. It is shown that these classes are stable under…

Let X_1, X_2,..., X_n be a sequence of independent random variables, let M be a rearrangement invariant space on the underlying probability space, and let N be a symmetric sequence space. This paper gives an approximate formula for the…

This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length…