Limit Theorems of Probability TheoryPál Révész, Bolyai János Matematikai Társulat North-Holland Publishing Company, 1975 - 420 páginas Limit laws for order statistics; Some notes on the law of the iterated logarithm for empirical distribution function; Some notes on the empirical distribution function and the quantile process; Law of large numbers for Markov chains homogeneous in time and in the second component; Learning from an ergodic training sequence; Around the Glivenko - Cantelli theorem; Gauss distributions and central limit theorem for locally compact groups; Limit problems on topological stochastic groups and bohr compactification; Weak convergence and embedding; The method of perturbation on the spectrum of linear operators in asymptotic problems of probability theory; Equivalence-orthogonality dichotomies of probability measures; On some asymptotical properties of recursive estimates; On the properties of the recursive estimates for a functional of an unknown distribution function; Some functional laws of the iterated logarithm for dependent random variables. |
Conteúdo
CONTENTS | 7 |
33333 | 73 |
J Komlós P Major G Tusnády Weak convergence | 149 |
Direitos autorais | |
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a₁ arbitrary assume asymptotic bounded Brownian motion Budapest C₁ Cantelli central limit theorem COLLOQUIA MATHEMATICA SOCIETATIS condition convergence Corollary defined denote dependent random variables distribution function Erdős estimation exists F₁ finite Gauss distribution Gaussian group G Hence holds Hungary implies independent inequality Inst iterated logarithm JÁNOS BOLYAI JÁNOS BOLYAI 11 KESZTHELY KESZTHELY HUNGARY Lemma Let G Lévy Lie group lim sup limit distribution linear locally compact group log log log³n M¹(G Markov chain Math MATHEMATICA SOCIETATIS JÁNOS obtain order statistics P₁ positive constant probability measures probability space PROBABILITY THEORY Proc prove quantile random variables Remark result Révész satisfies semi group semi-Markov semi-Markov process sequence f(n,x sequence of random Smirnov SOCIETATIS JÁNOS BOLYAI stochastic Strassen T₁ T₂ Theorem 3.1 THEOREMS OF PROBABILITY tion unit ball verw X₁