Related papers: Asymptotic Stability of Empirical Processes and Re…
We aim at providing a characterization of the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven via a quasi-tangency…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
The empirical measure flow of a McKean-Vlasov $n$-particle system with common noise is a measure-valued process whose law solves an associated martingale problem. We obtain a stability result for the sequence of martingale problems: all…
The problem of estimating the exponent of a stable law received a considerable attention in the recent literature. Here, we deal with an estimate of such a exponent introduced by De Haan and Resnick when the corresponding distribution…
Let $T \colon M \to M$ be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let $v \colon M \to \mathbb{R}^d$ be an observable and $v_n = \sum_{k=0}^{n-1} v \circ T^k$ denote the Birkhoff sums. Given a…
We define susceptibilities as a measure of the response of an observable quantity of a parameterized statistical model to a perturbation of the data for a general class of observables. We define estimators for these susceptibilities as…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
This note studies (practical) asymptotic stability of nonlinear networked control systems whose protocols are not necessarily uniformly globally exponentially stable. In particular, we propose a Lyapunov-based approach to establish…
This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end…
We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…
The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…
As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…
Empirical likelihood approach is one of non-parametric statistical methods, which is applied to the hypothesis testing or construction of confidence regions for pivotal unknown quantities. This method has been applied to the case of…
For $\tau\in S_3$, let $\mu_n^{\tau}$ denote the uniformly random probability measure on the set of $\tau$-avoiding permutations in $S_n$. Let $\mathbb{N}^*=\mathbb{N}\cup\{\infty\}$ with an appropriate metric and denote by…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup…