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M. J. Ruzhylo, T. A. Skorokhod

On empirical distributions in spaces of growing dimensions. Discrete distributions

Consider a random vector x_n = (x ¹, ..., xⁿ ) in the space Rⁿ where {x^k, k ≤ n} are independent identically distributed random variables in R with a common distribution F(dx) in R . Denote by F_n the distribution of x_n . Let

{x_n (1), ... , x_n (m)}

be independent identically distributed vectors in Rⁿ with the common distribution F_n . We investigate asymptotic behavior of empirical distribution in Rⁿ which is determined by the relation

as n → ∞,m → ∞. The main tool of investigation is the theory of large deviation ( see: Richard S. Ellis, Entropy, Large Deviations and Statistical Mechanics ). We will consider finite discrete distributions F.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 13, 09/2005
Seiten: 265 - 280

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