156 citations · 398 across the 47 of their papers we have counts for
7 papers · 2 filters
Law of the iterated logarithm for the periodogram
Christophe Cuny, Florence Merlevède, Magda Peligrad
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram proper…
Empirical central limit theorems for ergodic automorphisms of the torus
J. Dedecker, F. Merlevède, F. Pène
Let T be an ergodic automorphism of the d-dimensional torus T^d, and f be a continuous function from T^d to R^l. On the probability space T^d equipped with the Lebesgue-Haar measur…
Strong invariance principles with rate for "reverse" martingales and applications
Christophe Cuny, Florence Merlevede
In this paper, we obtain almost sure invariance principles with rate of order , , for sums associated to a sequence of reverse martingale differences. Th…
Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus
J. Dedecker, F. Merlevède, F. Pène
In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodi…
A quenched weak invariance principle
Jérôme Dedecker, Florence Merlevède, Magda Peligrad
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to s…
Bernstein inequality and moderate deviations under strong mixing conditions
Florence Merlevède, Magda Peligrad, Emmanuel Rio
In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bou…