Related papers: Limit theorems for chains with unbounded variable …
The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
Consider the normalized partial sums of a real-valued function $F$ of a Markov chain, \[\phi_n:=n^{-1}\sum_{k=0}^{n-1}F(\Phi(k)),\qquad n\ge1.\] The chain $\{\Phi(k):k\ge0\}$ takes values in a general state space $\mathsf {X}$, with…
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on…
Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…
Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…
The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables…
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…
We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infnite memory chains for which the family of transition probabilities is represented by a probabilistic…
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…
We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…
We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…
For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the asymptotic behavior of the set of allowed cycle lengths, we…
We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
We introduce a class of absorption mechanisms and study the behavior of real-valued centered random walks with finite variance that do not get absorbed. In particular, we prove persistence and scaling limit results, which, in many cases of…
This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald…
Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.