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安徽师范大学概率论与数理统计课件Chapter3 Random Vectors and their Numerical Characteristics
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...
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...
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...
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...
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...
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
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 ...
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...
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...

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