92 research outputs found
Central limit theorem and Diophantine approximations
Let denote the distribution function of the normalized sum of i.i.d. random variables with finite fourth
absolute moment. In this paper, polynomial rates of convergence of to the
normal law with respect to the Kolmogorov distance, as well as polynomial
approximations of by the Edgeworth corrections (modulo logarithmically
growing factors in ) are given in terms of the characteristic function of
. Particular cases of the problem are discussed in connection with
Diophantine approximations
Concentration of the information in data with log-concave distributions
A concentration property of the functional is demonstrated,
when a random vector X has a log-concave density f on . This
concentration property implies in particular an extension of the
Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time
stochastic processes with log-concave marginals.Comment: Published in at http://dx.doi.org/10.1214/10-AOP592 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Hyperbolic Measures on Infinite Dimensional Spaces
Localization and dilation procedures are discussed for infinite dimensional
-concave measures on abstract locally convex spaces (following Borell's
hierarchy of hyperbolic measures).Comment: 25 Page
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