Large deviations

Tuesday, April 14, 2015 - 9:00am - 9:50am
Rafal Latala (University of Warsaw)
The fundamental result of Paouris gives the large deviation estimate for Euclidean norms of log-concave vectors. We extend it to the case of l_r-norms
and show that for r>=2, p>=1 the p-th moment of the l_r-norm of a log-concave random vector is comparable to the sum of the first moment and the weak p-th moment up to a constant proportional to r.

Joint work with Marta Strzelecka (University of Warsaw).
Tuesday, January 15, 2013 - 3:15pm - 4:05pm
Eric Vanden-Eijnden (New York University)
Tuesday, January 15, 2013 - 9:00am - 9:50am
Paul Dupuis (Brown University)
In this talk and a sequel given by Amarjit Budhiraja we will discuss how variational representations can be used to develop an efficient methodology for large deviations analysis, especially in the infinite dimensional setting. This talk will start by reviewing the use of representations in a simple setting. We then discuss the proof of representations for infinite dimensional Brownian motion, and an application to an estimation problem in image matching.
Wednesday, January 16, 2013 - 9:00am - 9:50am
Amarjit Budhiraja (University of North Carolina, Chapel Hill)
In this talk we consider Stochastic dynamical systems with jumps. Large deviation results for finite dimensional stochastic differential equations with a Poisson
noise term have been studied by several authors, however for infinite dimensional models
with jumps, very little is available. The goal of this work is to develop a systematic approach for the study of large deviation properties of such infinite dimensional systems.
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