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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...
A FUNCTIONAL HUNGARIAN CONSTRUCTION FOR SUMS OF INDEPENDENT RANDOM VARIABLES
Komlos-Major–Tusnády inequality Partial sum process Non-identically distributed variables Function classes Asymptotic equivalence of statistical experiments
2015/8/25
We develop a Hungarian construction for the partial sum process of independent non-identically distributed random variables. The process is indexed by functions f from a class H, but the supremum over...
On possible mixing rates for some strong mixing conditions for N-tuplewise independent random fields
Random field mixing conditions mixing rates N-tuplewise independence
2011/9/15
Abstract: For a given pair of positive integers $d$ and $N$ with $N \geq 2$, for strictly stationary random fields that are indexed by the $d$-dimensional integer lattice and satisfy $N$-tuplewise ind...
Extend the Borel-Cantelli lemma to sequences of non-independent random variables
Borel-cantelli Lemma Cauchy-schwarz Inequality
2010/9/21
In this paper we discus on the Borel-Cantelli lemma when the condition of independent events is replaced by negative quadrant dependent condition.
On the Asymptotic Spectrum of Products of Independent Random Matrices
Asymptotic Spectrum of Products Independent Random Matrices
2011/1/21
We consider products of independent random matrices with independent entries.The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let X()jk , 1 ≤...
Current fluctuations for independent random walks in multiple dimensions
Independent random walks hydrodynamic limit current Independent random walks
2010/12/6
Consider a system of particles evolving as independent and iden-tically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity ~v, the c...