Limit Distributions for Sums of Independent Random Variables |
Contents
PREFACE | 1 |
PROBABILITY DISTRIBUTIONS RANDOM VARIABLES | 13 |
DISTRIBUTIONS IN Rą AND THEIR CHARACTERISTIC FUNCTIONS ONS | 32 |
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B. V. Gnedenko Borel sets bounded variation characteristic function continuity points converge defined dFnj dFnj(y dG(y distribution function F(x distribution laws domain of attraction domain of partial elementary events equation exists fn(t Fn(x follows Gnedenko Hence identically distributed independent random variables inequality infinitely divisible law infinitesimal integral interval large numbers lattice distribution law F(x law of large Lebesgue integral LEMMA lim lim limit law limit theorems log f(t mathematical expectation measure necessary and sufficient normal distribution normal law obtained partial attraction Poisson law Proof proved satisfied sequence stable law Stieltjes integral sufficiently large suitably chosen constants summands sums of independent theory of probability tion Translator's note unimodal unimodal distribution values weak convergence xdFnk ζη μη ξη ξι