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Topics in probability theory are explained for a first-year graduate course. Necessary background material in measure theory is developed, and characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Both weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, and laws on the iterated logarithm. Material on dependent random variables discusses discrete parameter martingales, Doob's inequalities, and standard topics in Markov chains. The author is affiliated with Courant Institute of Mathematical Sciences. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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