Related papers: Central limit theorem for bifurcating Markov chain…

Whereas classical invariance principles for ergodic Markov chains address the situation in which the time horizon of observations is much larger than the mixing time, the quality of approximation is questionable when this is not the case…

We provide a simple proof for of the central limit theorem for the number of vertices in the giant for super-critical stochastic block model using the breadth-first walk of Konarovskyi, Limic and the author (2024). Our approach follows the…

A Central Limit Theorem for linear combinations of iterates of an inner function is proved. The main technical tool is Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures.

In this paper we investigate the local limit theorem for additive functionals of nonstationary Markov chains that converge in distribution. We consider both the lattice and the non-lattice cases. The results are also new in the stationary…

We consider sub-critical configuration models and show that the central limit theorem for any additive statistic holds when the statistics satisfies a fourth moment assumption, a variance lower bound and the degree sequence of graph…

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…

In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

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…

The main objective of this paper is to establish bootstrap uniform functional central limit theorem for Harris recurrent Markov chains over uniformly bounded classes of functions. We show that the result can be generalized also to the…

We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a functional central limit theorem for the properly rescaled…

Suppose that X_n, n>=0 is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observanle. We say that the observable satisfies the central limit theorem (C.L.T.) if Y_n:=N^{-1/2}\sum_{n=0}^NV(X_n)…

We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…

We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

Applying quantitative perturbation theory for linear operators, we prove non-asymptotic limit theorems for Markov chains whose transition kernel has a spectral gap in an arbitrary Banach algebra of functions X . The main results are…

We establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic, using the Perron-Frobenius operator. We apply the result to asymptotically periodic transformations and…

In this paper, we study the quenched central limit theorem for the discrete Fourier transform. We show that the Fourier transform of a stationary ergodic process, suitable centered and normalized, satisfies the quenched CLT conditioned by…

In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…