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We obtain the first results on convergence rates in the Prokhorov metric for the weak invariance principle (functional central limit theorem) for deterministic dynamical systems. Our results hold for uniformly expanding/hyperbolic (Axiom A)…

Dynamical Systems · Mathematics 2021-07-28 Marios Antoniou , Ian Melbourne

We investigate the convergence rates of the trajectories generated by implicit first and second order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz…

Optimization and Control · Mathematics 2015-04-09 Radu Ioan Bot , Ernö Robert Csetnek

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…

Dynamical Systems · Mathematics 2016-03-25 Peter Nandori , Domokos Szasz , Tamas Varju

For each $n \geq 1$, let $\{X_{j,n}\}_{1 \leq j \leq n}$ be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process…

Probability · Mathematics 2008-05-28 Raluca Balan , Sana Louhichi

We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of…

Statistics Theory · Mathematics 2016-05-18 Jérôme Dedecker , Florence Merlevède

We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…

Probability · Mathematics 2025-12-18 Attila Lovas , Miklós Rásonyi , Lionel Truquet

The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…

Probability · Mathematics 2011-10-20 Katarzyna Bartkiewicz , Adam Jakubowski , Thomas Mikosch , Olivier Wintenberger

In this paper we study some asymptotic properties of the kernel conditional quantile estimator with randomly left-truncated data which exhibit some kind of dependence. We extend the result obtained by Lemdani, Ould-Sa\"id and Poulin [16] in…

Statistics Theory · Mathematics 2008-10-08 Elias Ould-Saïd , Djabrane Yahia , Abdelhakim Necir

We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of…

Probability · Mathematics 2008-10-06 Oliver Johnson

In this work we investigate the asymptotic behaviour of weighted partial sums of a particular class of random variables related to Oppenheim series expansions. More precisely, we verify convergence in probability as well as almost sure…

Probability · Mathematics 2020-04-08 Rita Giuliano , Milto Hadjikyriakou

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Analysis of PDEs · Mathematics 2020-09-04 Prakash Kumar Das , M. M. Panja

We obtain rates of convergence in the weak invariance principle (functional central limit theorem) for $\R^d$-valued H\"older observables of nonuniformly hyperbolic maps. In particular, for maps modelled by a Young tower with…

Dynamical Systems · Mathematics 2025-03-21 Nicholas Fleming-Vázquez

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

Probability · Mathematics 2021-09-07 Richard C. Bradley , Zbigniew J. Jurek

Let T be an ergodic automorphism of the d-dimensional torus. In the spirit of Le Borgne, we give conditions on the Fourier coeffi cients of a real valued function f under which the Birkhoff sums satis fy a strong invariance principle. Next,…

Dynamical Systems · Mathematics 2012-06-21 Jérôme Dedecker , Florence Merlevède , Francoise Pene

We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds…

Probability · Mathematics 2015-07-13 Xiequan Fan , Ion Grama , Quansheng Liu

Let $X$ be a continuous-time strongly mixing or weakly dependent process and $T$ a renewal process independent of $X$ with inter-arrival times $\tau$. We show general conditions under which the sampled process $(X_{T_i},T_i-T_{i-1})^{\top}$…

Statistics Theory · Mathematics 2022-02-02 Dirk-Philip Brandes , Imma Valentina Curato , Robert Stelzer

In this paper, we consider the convergence rate with respect to Wasserstein distance in the invariance principle for deterministic nonuniformly hyperbolic systems, where both discrete time systems and flows are included. Our results apply…

Dynamical Systems · Mathematics 2023-01-04 Zhenxin Liu , Zhe Wang

This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…

Optimization and Control · Mathematics 2021-12-13 Boris S. Mordukhovich , Pedro Pérez-Aros

The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…

Probability · Mathematics 2023-10-03 Rita Giuliano , Milto Hadjikyriakou

We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…

Dynamical Systems · Mathematics 2020-05-14 Yeor Hafouta