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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Common terms and phrases
Akad Appl asymptotic expansions Banach spaces bounds Bulinskii central limit theorem coefficients condition convergence rate Cramér cumulants denotes dependent r.v.'s distribution function distributions of sums Dokl English transl estimate exists finite fn(t Gaussian Götze Hilbert space Hölder's inequality Ibragimov identically distributed independent random variables inequality infinite-dimensional integral invariance principle iterated logarithm large deviation probabilities large deviations large numbers law of large Lemma Liet Lith m-dependent Markov chain Math method metric mixing sequences Nagaev Nauk obtain Paulauskas Petrov polynomial Primen Prokhorov proved random fields rate of convergence remainder term Rink Russian satisfies Saulis Sazonov sequence of independent spectral stationary Statist Statulevičius sums of independent Sunklodas Suppose Teor theorems for sums Theory Probab ti+1 Veroyatn Vilnius Wahrscheinlichkeitstheorie Verw weakly dependent random Zalesskii Zitikis
References to this book
Teubner-Taschenbuch der Stochastik: Wahrscheinlichkeitstheorie ... Frank Beichelt,Douglas C. Montgomery No preview available - 2013 |