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20 papers · 1 filter
An empirical central limit theorem in L^1 for stationary sequences
Sophie Dede
In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary seq…
High-dimensional stochastic optimization with the generalized Dantzig estimator
Karim Lounici
We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case…
Large deviations for Branching Processes in Random Environment
Vincent Bansaye, Julien Berestycki
A branching process in random environment is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this…
Stein's method and stochastic analysis of Rademacher functionals
Ivan Nourdin, Giovanni Peccati, Gesine Reinert
We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein's method, as well as the use of appropriate discre…
From Black-Scholes and Dupire formulae to last passage times of local martingales. Part B : The finite time horizon
Amel Bentata, Marc Yor
These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics stu…
On a surprising relation between rectangular and square free convolutions
Florent Benaych-Georges
Debbah and Ryan have recently proved a result about the limit empirical singular distribution of the sum of two rectangular random matrices whose dimensions tend to infinity. In th…