Related papers: Bootstrap Central Limit Theorem for Chains of Infi…
We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.
In this note, a general approach to the study of non-stationary Markov chains with catastrophes and the corresponding queuing models is considered, as well as to obtain estimates of the limiting regime itself. As an illustration, an example…
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…
The purpose of this work is to establish a central limit theorem that can be applied to a particular form of Markov chains, including the number of descents in a random permutation of $\mathfrak{S}_n$, two-type generalized P{\'o}lya urns,…
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…
Bootstrap is a principled and powerful frequentist statistical tool for uncertainty quantification. Unfortunately, standard bootstrap methods are computationally intensive due to the need of drawing a large i.i.d. bootstrap sample to…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…
In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…
In 1956, Dobrushin proved a definitive central limit theorem for non-homogeneous Markov chains. In this note, a shorter and different proof elucidating more the assumptions is given through martingale approximation.
We study the limiting object of a sequence of Markov chains analogous to the limits of graphs, hypergraphs, and other objects which have been studied. Following a suggestion of Aldous, we assign to a sequence of finite Markov chains with…
The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the…
Markov chain approximations of symmetric jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a symmetric jump process with state space $\mathbbm{R}^d$ the…
We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric…
We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block bootstrap and for the tapered block bootstrap, and show…
We study the bootstrap for the maxima of the sums of independent random variables, a problem of high relevance to many applications in modern statistics. Since the consistency of bootstrap was justified by Gaussian approximation in…
Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…
We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a…
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…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…