相关论文: Elementary Proofs of the Main Limit Theorems of Pr…

The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…

We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…

Consider the boundary case in a one-dimensional super-critical branching random walk. It is known that upon the survival of the system, the minimal position after $n$ steps behaves in probability like ${3\over 2} \log n$ when $n\to \infty$.…

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…

This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…

We discuss a complementary asymptotic analysis of the so called minimal random walk. More precisely, we present a version of the almost sure central limit theorem as well as a generalization of the recently proposed quadratic strong laws.…

An essential component of inference based on familiar frequentist notions, such as $p$-values, significance and confidence levels, is the relevant sampling distribution. This feature results in violations of a principle known as the strong…

We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type central limit theorem for the empirical distributions, thus…

We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions, the finite-dimensional distributions of G_t converge weakly…

We determine the distributional behavior for products of free random variables in a general infinitesimal triangular array. In the case of positive variables, the main theorem extends a result proved earlier for arrays with identically…

The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…

An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…

The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…

Let $(X_i)_{i \geq 1}$ and $(Y_i)_{i\geq1}$ be two independent sequences of independent identically distributed random variables taking their values in a common finite alphabet and having the same law. Let $LC_n$ be the length of the…

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…

In the seminal contribution [4] the joint weak convergence of maxima and minima of weakly dependent stationary sequences is derived under some mild asymptotic conditions. In this paper we address additionally the case of incomplete samples…

We prove a conjecture of Toth and Veto about the weak convergence of the self repelling random walk with directed edges under diffusive scaling to a uniform distribution.

We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…