Related papers: On some Limit Theorem for Markov Chain

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…

We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…

We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation. We use the result to…

We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two…

We prove a central limit theorem for random walks with finite variance on linear groups.

We prove the Central Limit Theorem for linear statistics of the eigenvalues of band random matrices provided $\sqrt{n} \ll b_n \ll n$ and test functions are sufficiently smooth.

In this paper, we obtain an explicit total variation bound in the central limit theorem for the sums of non-i.i.d. random variables. Our results show that, under suitable assumptions, Lindeberg's condition is sufficient and necessary for…

In this paper we study the almost sure central limit theorem started from a point for additive functionals of a stationary and ergodic Markov chain via a martingale approximation in the almost sure sense. As a consequence we derive the…

By the Lindeberg-L\'evy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual…

We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions. The conditions imposed on the transition…

We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the…

In this paper we consider a sequence of random variables with mean uncertainty in a sublinear expectation space. Without the hypothesis of identical distributions, we show a new central limit theorem under the sublinear expectations.

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…

We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale…

Let $(X_i)$ be a stationary and ergodic Markov chain with kernel $Q$, $f$ an $L^2$ function on its state space. If $Q$ is a normal operator and $f = (I-Q)^{1/2}g$ (which is equivalent to the convergence of $\sum_{n=1}^\infty…

Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…

This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…

We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy…

Let $Q$ be a transition probability on a measurable space $E$ which admits an invariant probability measure, let $(X_n)_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S_n=\sum…