Limit Theorems of Probability Theory
Sequences of Independent Random Variables
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The aim of the book is two-fold. First, the book can be a basis for a course in probability for graduate or advanced undergraduate students. Second, the book can serve as a reference formulations of many (mostly recent) results which are usually inaccessible in book form. These supplements border on the basic text and make it possible for the reader to look at the frontier of modern investigations.
This book offers a superb overview of limit theorems and probability inequalities for sums of independent random variables. Unique in its combination of both classic and recent results, the book details the many practical aspects of these important tools for solving a great variety of problems in probability and statistics. Topics include limit theorems on convergence to infinitely divisible distributions, the central limit theorem with rates of convergence, the weak and strong law of large numbers, the law of the iterated logarithm, and the many inequalities for sums of an arbitrary number random variables. Ideal as both a graduate text and a reference for seasoned mathematicians, Limit Theorems of Probability Theory brings the reader to the frontier of current research.
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