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It is shown that for every sequence (x,) of elements of 1'; the following two properties are equivalent: (4 bJk1 12 UTI. (b) (lS,/nllz, FJ is a quasimartingale, where S, = E,x,, (4 being a sequenc...
We prove that for a Radernacher sequence (r,) and any sequence of real numbers [ad the inequality holds true.
This paper is devoted to the interpretation of condition (i). For instance, it is shown that if the r.v. X, are weighted Rademacher r.v., then (i) is equivalent to the fact that ((S,/n)', %A is a qu...
A distribution of an a-spherical random vector is shown to be uniquely determined by a distribution of quotients
In this paper we consider a Bernstein property of probability measures on groups introduced by Neuenschwander. We discuss this property for discrete groups, compact groups, nilpotent groups and som...
In this note, which develops a part of our paper [2], we consider independence properties between Brownian motion, after Brownian scaling on a random interval (a, b), and the length (b-a) of the in...
The paper gives some insight into the relations between two types of Markov processes – in the strict sense and in the wide sense – as well as into two aspects of periodicity. It concerns Markov pro...
Positivity of the prior probability of Kullback-Leibler neighborhood around the true density, commonly known as the Kullback-Leibler property, plays a fundamental role in posterior consistency. A popu...
We derive the l∞ convergence rate simultaneously for Lasso and Dantzig estimators in a high-dimensional linear regression model under a mutual coherence assumption on the Gram matrix of the design and...
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to: 1. A...
We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the or...
We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the or...
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by R 10 Xs...
We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges’ estimator. The or...

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