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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...
Strong exponential integrability of sums of independent B-valued random vectors
Strong exponential integrability sums of independent B-valued random vectors
2009/9/24
Strong exponential integrability of sums of independent B-valued random vectors。
A roumula for the density of the norm of stable random vectors in Hilbert spaces
the density of the norm stable random vectors Hilbert spaces
2009/9/23
A roumula for the density of the norm of stable random vectors in Hilbert spaces。
Complements on decoupling inequalities for multilinear functions in stable random vectors
decoupling inequalities multilinear functions stable random vectors
2009/9/23
Complements on decoupling inequalities for multilinear functions in stable random vectors。
Comparison of sums of independent identically distributed random vectors
Comparison sums of independent identically distributed random vectors
2009/9/23
Comparison of sums of independent identically distributed random vectors。
For a symmetric a-stable random vector (XI.,. . , X,,X ,+ ,)
with 1 < a < 2 and spectral measure r, we find a necessary and
sufficient condition in terms of r for the conditional variance
Var(X,+l ...
Weak convergence of random vectors and distributions in Banach spaces
Distributions in Banach spaces weak limits of random vectors weak limits of distributions
2009/9/21
Let (5,J be a sequence of random vectors with values in
a Banach space X with distributions pen weakly converging to a given
distribution p. We characterize a general form of a distribution of
a we...
Some remarks on S alpha S,beta - substable random vectors
Symmetric u-stable vector substable distributions spectral measure
2009/9/21
An SorS random vector X is pserbstable, or < fl d 2,
if X: YeiM for some symmetric /?-stable random vector Y, 8 3 0
a random variable with the Laplace transform exp {-@), Y and
B are independent. W...
Multivariate large deviations for sums of i.i.d. random vectors with compactly supported distribution
Abel theorem Cramkr transfonnatiou Fenchel-Legendre transformation Laplace method
2009/9/21
The sums of i.i.d. random vectors with compactly supported
and absolutely continuous distribution are considered. Under
some conditions the strong form of the local limit theorem for large
deviatio...
Coamparision of tail probabilities of strictly stable/stable random vectors and their symmetrized counterparts with application
Stable emistable nequality
2009/9/21
It is shown that the tail probabilities of a strictly
(r, a)-semistable (0 < r < 1,0 < n < 2, a # 1) Banach space valued random
vector X and its symmetrized counterpart are "uniformly" comparable
i...