Christophe Cuny

On martingale approximations and the quenched weak invariance principle

In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in

ERGODIC THEOREMS WITH ARITHMETICAL WEIGHTS

\h

On the a. s. convergence of the one-sided ergodic Hilbert transform

(a real and separable Hilbert space) admits an approximation, in

On random almost periodic trigonometric polynomials and applications to ergodic theory

\LL^p (\h)

On random almost periodic series and random ergodic theory

,

An alternative to the coupling of Berkes-Liu-Wu for strong approximations

p>1

On Nörlund summation and ergodic theory, with applications to power series of Hilbert contractions

, by a martingale with stationary differences and we then estimate the error of approximation in

Invariance principles under the Maxwell–Woodroofe condition in Banach spaces

\LL^p (\h)

Central Limit Theorem Started at a Point for Stationary Processes and Additive Functionals of Reversible Markov Chains

. The results are exploited to further investigate the behavior of the partial sums. In particular we obtain new projective conditions concerning the Marcinkiewicz-Zygmund theorem, the moderate deviations principle and the rates in the central limit theorem in terms of Wasserstein distances. The conditions are well suited for a large variety of examples including linear processes or various kinds of weak dependent or mixing processes. In addition, our approach suits well to investigate the quenched central limit theorem and its invariance principle via martingale approximation, and allows us to show that they hold under the so-called Maxwell-Woodroofe condition that is known to be optimal.

Strong Invariance Principles with Rate for “Reverse” Martingale Differences and Applications

AbstractWe prove that the divisor function d(n) counting the number of divisors of the integer n is a good weighting function for the pointwise ergodic theorem. For any measurable dynamical system (X, A, ν, τ) and any f ∈ Lp(ν), p > 1, the limit