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We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of...
Methodes de changement de temps pour la convergence en loi des martingales
Azema martingales with drift      Azema martingales  drift       2009/9/22
Pursuing the earlier work of Emery [I], Meyer [2], [3] and the author [4] it is shown that Akma martingales starting from a varying initial point on the line constitute an Evans-Hudson flow in the ...
We investigate independent marginals of full operator- semistable and operator-stable probability measures on linite- -dimensional vector spaces. In particular, it is shown that for purely Poissoni...
For the absolutely @-summing operators T: X + Y between Banach spaces X and Y we consider martingale inequalities of the type where (dR)F='=c, L: (R, f,P) is a martingale difference sequence and (...
Pseudo-martingales      Pseudo-martingales        2009/9/22
For a probability space (n, F, P) and a filtration (a,,) in R, we consider the sequences (X,) of random variables satisfying the condition ( X + - X 1 ) 0 n = 1, 2, ... In general, the process (X,...
We prove a contraction principle for vector-valued martingales of type where X is a Banach space with elements x,, . . ., x,,, (A& c Ll (9, P) a martingale difference sequence belonging to a certai...
We establish new almost sure properties for powers of weighted martingale transbrms. It allows us to deduce usefuI asymptotic results for cumulative prediction and estimation errors associated with...
Some random times and martingales associated with BES0(δ) processes (0<δ<2).
We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, conver...
Consider a martingale $M$ with bounded jumps and two sequences $a_n, b_n to infty$. We show that if the rescaled martingales M^n_t =frac{1}{sqrt{a_n}}M_{b_n t} converge weakly, then the limit is...
Let $X=(X_t)_{tgeq 0}$ be a martingale and $H=(H_t)_{tgeq 0}$ be a predictable process taking values in $[-1,1]$. Let $Y$ denote the stochastic integral of $H$ with respect to $X$. We show that $$ ||s...
We show, by a simple counterexample, that the main result in a recent paper by H. Van Zanten [Electronic Communications in Probability 7 (2002), 215-222] is false. We eventually point out the origin o...

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