Moving Shift Averages for Ergodic Transformations.
Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries
In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided.
Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments
Multidimensional version of the results of Komlos, Major and Tusnady for vectors with finite exponential moments
A multidimensional version of the results of Komlos, Major and Tusnady for the Gaussian approximation of the sequence of successive sums of independent random vectors with finite exponential moments is obtained.
Multiparameter pointwise ergodic theorems for Markov operators on L∞.
Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p < ∞ the averagesAnf = (n + 1)-d Σ0≤ni≤n P1n1 P2n2 ... Pdnd f (n ≥ 0)converge almost everywhere if and only if there exists an invariant and equivalent finite measure λ for which the Radon-Nikodym derivative v = dλ/dμ is in the dual space Lp'(X,F,μ). Next we study the case in...
Multiple recurrence for discrete time Markov processes. II
Multivariate normal approximation using Stein’s method and Malliavin calculus
We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of gaussian fields. Among several examples, we provide an application to a functional version of the Breuer–Major CLT for fields subordinated to a fractional brownian motion.
Multivariate tail equivalence of distributions in extreme value theory