Related papers: Limit theorems for chains with unbounded variable …
The weak and strong laws of large numbers for time-inhomogeneous Markov chains are studied under general conditions. First, under Drift Condition and Contraction Condition in total variation, we prove the weak law of large numbers. Then,…
We use a generalized form of Dyson's spin wave formalism to prove several central limit theorems for the large-spin asymptotics of quantum spins in a coherent state.
The Central Limit Theorem (CLT) for additive functionals of Markov chains is a well known result with a long history. In this paper we present applications to two finite-memory versions of the Elephant Random Walk, solving a problem from…
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
We establish a central limit theorem (CLT) for families of products of $\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework…
We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques…
For certain random variables that arise as limits of functionals of random finite trees, we obtain precise asymptotics for the logarithm of the right-hand tail. Our results are based on the facts (i) that the random variables we study can…
In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a…
This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…
This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \(\xiv\) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The…
In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the…
We use the Cramer-Rao bound to show which short magnetic reversals can be recovered successfully from a magnetic anomaly profile. Using a simple variant of the Vine-Matthews model, we show, in particular, that errors in determining the…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…
We prove an asymptotic Cram\'er's theorem, that is, if the sequence $(X_{n}+ Y_{n})_{n\geq 1}$ converges in law to the standard normal distribution and for every $n\geq 1$ the random variables $X_{n}$ and $Y_{n}$ are independent, then…
For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…
We establish the weak large deviations principle for empirical measures of Markov chains on $\mathbb R^d$ under mild assumptions. In particular, no irreducibility is assumed and the initial measure may be arbitrary. The proof is entirely…
We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture the distribution of…