Related papers: An Almost Sure Invariance Principle for Additive F…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an i.i.d. process. A key step is to show that any…

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…

We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…

This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and P\"otscher (2007). More specifically, their…

The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…

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.

The Importance Markov chain is a novel algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain…

This paper introduces ergodic-risk criteria, which capture long-term cumulative risks associated with controlled Markov chains through probabilistic limit theorems--in contrast to existing methods that require assumptions of either finite…

In this note we (in particular) prove an almost sure invariance principle (ASIP) for non-stationary and uniformly bounded sequences of random variables which are exponentially fast $\phi$-mixing. The obtained rate is of order…

We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local…

We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…

We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…

The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M.…

In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a long time. In this…

The aim of this paper is to prove that Markov's theorem on variation of zeros of orthogonal polynomials on the real line [Math. Ann., 27:177-182,1886] remains essentially valid in the case of paraorthogonal polynomials on the unit circle.