Related papers: A Useful Version of the Central Limit Theorem for …
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…
The goal of this expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains. This is done with a view towards Markov chain Monte Carlo settings and hence the focus…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are…
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…
This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded…
A new sufficient condition is proposed in the problem of Central Limit Theorem in the array scheme for non-homogeneous Markov Chains.
We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin (1956) for temporally…
We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system…
This paper aims to establish a central limit theorem for Markov processes conditioned not to be absorbed under a very general assumption on quasi-stationarity for the underlying process. To do so, a central limit theorem has been…
In this paper we study the central limit theorem for additive functionals of stationary Markov chains with general state space by using a new idea involving conditioning with respect to both the past and future of the chain. Practically, we…
This is a note on some results of the central limit theorem for deterministic dynamical systems. First, we give the central limit theorem for martingales, which is a main tool. Then we give the main results on the central limit theorem in…
This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated…
For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a…
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…
Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore,…
In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This…
The central limit theorem for Markov chains generated by iterated function systems consisting of orientation preserving homeomorphisms of the interval is proved. We study also ergodicity of such systems.
A new version of a sufficient condition of a Dobrushin type is proposed for non-homogeneous Markov chains for a certain class of such processes. The original Dobrushin's condition may fail, yet, the CLT is still valid
In this paper we give sufficient conditions for the almost sure central limit theorem started at a point, known under the name of quenched central limit theorem. This is achieved by using a new idea of conditioning with respect to both the…