Related papers: Effective limit theorems for Markov chains with a …
We consider two examples for a well-known method for obtaining concentration of measure (COM) bounds for a given observable in a given measure. The method is to consider an auxiliary Markov chain for which the invariant distribution is the…
We consider a Markov chain $\{X_n\}_{n=0}^\8$ on $\R^d$ defined by the stochastic recursion $X_{n}=M_n X_{n-1}+Q_n$, where $(Q_n,M_n)$ are i.i.d. random variables taking values in the affine group $H=\R^d\rtimes {\rm GL}(\R^d)$. Assume that…
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.
Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a…
We provide bounds of Berry-Esseen type for fundamental limit theorems in operator-valued free probability theory such as the operator-valued free Central Limit Theorem and the asymptotic behaviour of distributions of operator-valued…
We consider nonparametric estimation of the transition operator $P$ of a Markov chain and its transition density $p$ where the singular values of $P$ are assumed to decay exponentially fast. This is for instance the case for periodised,…
Suppose that $\{X_t,\,t\ge0\}$ is a non-stationary Markov process, taking values in a Polish metric space $E$. We prove the law of large numbers and central limit theorem for an additive functional of the form $\int_0^T\psi(X_s)ds$,…
We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the…
Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class of quantum channels described by S. Attal et al. We consider…
The spectral gap $\gamma$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to…
The spectral gap $\gamma$ of an ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary…
In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the…
The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be…
We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds $L^\infty$ and the transformation fails to be Markov. Constructing a family…
Consider the set of all sequences of $n$ outcomes, each taking one of $m$ values, that satisfy a number of linear constraints. If $m$ is fixed while $n$ increases, most sequences that satisfy the constraints result in frequency vectors…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
We prove a Berry-Esseen theorem and Edgeworth expansions for partial sums of the form $S_N=\sum_{n=1}^{N}f_n(X_n,X_{n+1})$, where $\{X_n\}$ is a uniformly elliptic inhomogeneous Markov chain and $\{f_n\}$ is a sequence of uniformly bounded…
We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…