Related papers: Constant prediction and evasion number, I: General…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…
We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…
We use the concept of excursions for the prediction of random variables without any moment existence assumptions. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted…
In this paper we present a simplified model of a proportional taxation system where citizens decide whether to pay taxes or evade them. We initially derive a dynamic equation for the fraction of evaders and then present both its critical…
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…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system…
We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…
Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the…
We find, in the form of a continued fraction, the generating function for the number of (132)-avoiding permutations that have a given number of (123) patterns, and show how to extend this to permutations that have exactly one (132) pattern.…
There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…
Let $\mathcal{C}_n$ denote the set of words $w=w_1\cdots w_n$ on the alphabet of positive integers satisfying $w_{i+1}\leq w_i+1$ for $1 \leq i \leq n-1$ with $w_1=1$. The members of $\mathcal{C}_n$ are known as Catalan words and are…
Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
A subgroup G \leq Z^omega exhibits the Specker phenomenon if every homomorphism G \to Z maps almost all unit vectors to 0. We give several combinatorial characterizations of the cardinal se, the size of the smallest G \leq Z^omega…