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A LOCAL LIMIT THEOREM FOR SUMS OF INDEPENDENT RANDOM VECTORS
THEOREM FOR SUMS INDEPENDENT RANDOM
2015/9/29
We prove a local limit the sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bo...
Tail estimates for norms of sums of log-concave random vectors
log-concave random vectors concentration inequalities deviation inequalities random matrices
2011/9/15
Abstract: We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the nor...
Effect of truncation on large deviations for heavy-tailed random vectors
heavy tails truncation regular variation large deviation
2011/9/5
Abstract: This paper studies the effect of truncation on the large deviations behavior of the partial sum of a triangular array coming from a truncated power law model. Each row of the triangular arra...
A generalized Isserlis theorem for location mixtures of Gaussian random vectors
Isserlis theorem normal-variance mixture generalized hyperbolic distribution
2011/9/2
Abstract: In a recent paper, Michalowicz et al. provide an extension of Isserlis theorem to the case of a Bernoulli location mixture of a Gaussian vector. We extend here this result to the case of any...
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotyp...
Two dimensional Meixner random vectors of class ${\mathcal M}_L$
commutator annihilation operator creation operator preservation operator
2010/11/29
The paper is divided into two parts. In the first part we
lay down the foundation for defining the joint annihilation–preservation–creation decomposition of a finite family of, not necessarily commut...