相关论文: Exact convergence order of the $L_r$-quantization …

Under continuity and recurrence assumptions, we prove that the iteration of successive partial symmetrizations that form a time-homogeneous Markov process, converges to a symmetrization. We cover several settings, including the…

We are interested in proposing approximations of a sequence of probability measures in the convex order by finitely supported probability measures still in the convex order. We propose to alternate transitions according to a martingale…

A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite sub-matrices of an infinite nonnegative…

Let $ r, s>0 $. For a given probability measure $P$ on $\mathbb{R}^d$, let $(\alpha_n)_{n \geq 1}$ be a sequence of (asymptotically) $L^r(P)$- optimal quantizers. For all $\mu \in \mathbb{R}^d $ and for every $\theta >0$, one defines the…

We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a…

Let $(f_i)_{i=1}^N$ be a family of contractive similitudes on $\mathbb{R}^q$ satisfying the open set condition. Let $(p_i)_{i=0}^N$ be a probability vector with $p_i>0$ for all $i=0,1,\ldots,N$. We study the asymptotic geometric mean errors…

We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…

In this paper, we answer the question of equivalence, or singularity, of two given quasi-stationary Markov measures on one-sided infinite words, and the corresponding question of equivalence of associated Cuntz algebra $\O_N$…

Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…

Let $\mu_N$ be the empirical measure associated to a $N$-sample of a given probability distribution $\mu$ on $\mathbb{R}^d$. We are interested in the rate of convergence of $\mu_N$ to $\mu$, when measured in the Wasserstein distance of…

We demonstrate that all good asymptotic entanglement measures are either identical or place a different ordering on the set of all quantum states.

This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…

Optimal transport maps and plans between two absolutely continuous measures $\mu$ and $\nu$ can be approximated by solving semi-discrete or fully-discrete optimal transport problems. These two problems ensue from approximating $\mu$ or both…

We calculate exact convergence times to reach random bipartite entanglement for various random protocols. The eigenproblem of a Markovian chain governing the process is mapped to a spin chain, thereby obtaining exact expression for the gap…

Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…

Let $E$ be a Bedford-McMullen carpet determined by a set of affine mappings $(f_{ij})_{(i,j)\in G}$ and $\mu$ a self-affine measure on $E$ associated with a probability vector $(p_{ij})_{(i,j)\in G}$. We prove that, for every…

We study time-inhomogeneous Markov chains to obtain quantitative results on their asymptotic behavior. We use Poincar\'e, Nash, and logarithmic-Sobolev inequalities. We assume that our Markov chain admits a finite invariant measure at each…

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…

We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a…

The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which…