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PAC-Bayesian Analysis of Martingales and Multiarmed Bandits
PAC-Bayesian Analysis Martingales Multiarmed Bandits
2011/6/21
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...
Moderate Deviations for Martingales with Bounded Jumps
Moderate deviations martingales bounded martingale difference
2009/5/11
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...
Continuous Ocone Martingales as Weak Limits of Rescaled Martingales
ocone martingales rescaled martingales weak convergence
2009/4/29
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...
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...