## Limit Theorems of Probability TheoryThis book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems. The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results. The presentation dwells on three basic topics: the central limit theorem, laws of large numbers and the law of the iterated logarithm for sequences of real-valued random variables. The second part, "The Accuracy of Gaussian Approximation in Banach Spaces" (V. Bentkus, F. G6tze, V. Paulauskas and A. Rackauskas), reviews various results and methods used to estimate the convergence rate in the central limit theorem and to construct asymptotic expansions in infinite-dimensional spaces. The authors con fine themselves to independent and identically distributed random variables. They do not strive to be exhaustive or to obtain the most general results; their aim is merely to point out the differences from the finite-dimensional case and to explain certain new phenomena related to the more complex structure of Banach spaces. Also reflected here is the growing tendency in recent years to apply results obtained for Banach spaces to asymptotic problems of statistics. |

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addition Appl apply approximation assume asymptotic expansions Banach spaces Bentkus bounds central limit theorem coefficients condition consequence consider constant continuous convergence rate cumulants defined denotes derivatives differential distribution function Dokl English transl estimate example exists finite Gaussian given Götze Hilbert space holds identically independent random variables inequality infinite-dimensional integral large deviations Lemma Liet Lith m-dependent Markov chain Math means measure method metric mixing moments Nauk normal numbers obtain operator Paulauskas Petrov positive Primen processes proof proved Račkauskas random fields rate of convergence relation respect Rink Russian satisfies Saulis Sazonov sequence sequence of independent spectral stationary Statist Statulevičius strong sufficient sums of independent Suppose Teor Theory Probab values Veroyatn Vilnius Wahrscheinlichkeitstheorie Verw weakly dependent Zalesskii

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Teubner-Taschenbuch der Stochastik: Wahrscheinlichkeitstheorie ... Frank Beichelt,Douglas C. Montgomery No preview available - 2013 |