Related papers: Takacs' asymptotic theorem and its applications: A…

In statistical learning, models are classified as regular or singular depending on whether the mapping from parameters to probability distributions is injective. Most models with hierarchical structures or latent variables are singular, for…

This paper studies the properties of the probability density function $p_{\alpha,\nu, n}(\mathbf{x})$ of the $n$-variate generalized Linnik distribution whose characteristic function $\varphi_{\alpha,\nu,n}(\boldsymbol{t})$ is given by…

We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute…

We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…

We study distributions $F$ on $[0,\infty)$ such that for some $T\le\infty$, $F^{*2}(x,x+T]\sim 2 F(x,x+T]$. The case $T=\infty$ corresponds to $F$ being subexponential, and our analysis shows that the properties for $T<\infty$ are, in fact,…

We study a new technique for the asymptotic analysis of heavy-tailed systems conditioned on large deviations events. We illustrate our approach in the context of ruin events of multidimensional regularly varying random walks. Our approach…

The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…

We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…

In this paper we investigate the asymptotic statistical theory of irreducible quantum Markov chains, focusing on identifiability properties and asymptotic convergence of associated quantum statistical models. We show that the space of…

The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour of its solutions. Bertoin and Watson ($2018$) developed a probabilistic approach…

We prove several asymptotic results for partial and false theta functions arising from Jacobi forms, as the modular variable $\tau$ tends to $0$ along the imaginary axis, and the elliptic variable $z$ is unrestricted in the complex plane.…

This article studies the kinetic dynamics of the rock-paper-scissors binary game in a measure setting given by a non local and non linear integrodifferential equation. After proving the wellposedness of the equation, we provide a precise…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family…

Sarnak's Density Conjecture is an explicit bound on the multiplicities of non-tempered representations in a sequence of cocompact congruence arithmetic lattices in a semisimple Lie group, which is motivated by the work of Sarnak and Xue.…

The paper concerns the $d$-dimensional stochastic approximation recursion, $$ \theta_{n+1}= \theta_n + \alpha_{n + 1} f(\theta_n, \Phi_{n+1}) $$ where $ \{ \Phi_n \}$ is a stochastic process on a general state space, satisfying a…

Let $P_n$ and $Q_n$ be two probability measures representing two different probabilistic models of some system (e.g., an $n$-particle equilibrium system, a set of random graphs with $n$ vertices, or a stochastic process evolving over a time…

The paper by A.N. Kolmogorov 1934 "Random Moves", hereinafter ANK34, uses a Fokker-Planck-type equation for a 6-dimensional vector with a total rather than a partial derivative with respect to time, and with a Laplacian in the space of…

In this paper, we are interested in the asymptotic behaviour of the sequence of processes $(W_n(s,t))_{s,t\in[0,1]}$ with \begin{equation*} W_n(s,t):=\sum_{k=1}^{\lfloor nt\rfloor}\big(1_{\{\xi_{S_k}\leq s\}}-s\big) \end{equation*} where…

In this paper, we consider rational hypergeometric series of the form \[\frac{p}{\pi}= \sum_{k=0}^\infty u_k\quad\text{with}\quad u_k=\frac{\left(\frac{1}{2}\right)_k \left(q\right)_k \left(1-q\right)_k}{(k!)^3}(r+s\,k)\,t^k,\] where…