Related papers: Strong approximation of partial sums under depende…
Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\inA_{n} where the summands are i.i.d. and E_{n} is a…
We prove a weak iterated invariance principle for a large class of non-uniformly expanding random dynamical systems. In addition, we give a quenched homogenization result for fast-slow systems in the case when the fast component corresponds…
In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…
We study distributional properties of a quadratic form of a stationary functional time series under mild moment conditions. As an important application, we obtain consistency rates of estimators of spectral density operators and prove joint…
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
A family of random matrices is said to converge strongly to a limiting family of operators if the operator norm of every noncommutative polynomial of the matrices converges to that of the limiting operators. Recent developments surrounding…
We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a mixing condition on the covariate process transfers to a…
We give strong bounds for the rate of convergence of the regenerative process distribution to the stationary distribution in the total variation metric. These bounds are obtained by using coupling method. We propose this method for…
We construct strongly mixing invariant measures with full support for operators on F-spaces which satisfy the Frequent Hypercyclicity Criterion. For unilateral backward shifts on sequence spaces, a slight modification shows that one can…
Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence of $n^{-1/2}$ in the uniform metric, in other words, when…
Strong variational sufficiency is a newly proposed property, which turns out to be of great use in the convergence analysis of multiplier methods. However, what this property implies for non-polyhedral problems remains a puzzle. In this…
The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak…
We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
In the context of stationary $\mathbb{Z}^d$ nearest-neighbour Gibbs measures $\mu$ satisfying strong spatial mixing, we present a new combinatorial condition (the topological strong spatial mixing property (TSSM)) on the support of $\mu$…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…