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Limit Theorems of Probability Theory.pdf
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This 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 confine
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.
The third part ......
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