A Course in Probability Theory
Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.
While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.
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Chapter 1 Distribution function
Chapter 2 Measure theory
Chapter 3 Random variable Expectation Independence
Chapter 4 Convergence concepts
Chapter 5 Law of large numbers Random series
Chapter 6 Characteristic function
Chapter 7 Central limit theorem and its ramifications
½ 1g apply arbitrary assertion belongs Borel ﬁeld Borel measurable Borel set bounded called central limit theorem ch.f Chapter condition consequently consider constant convergence theorem converges a.e. converges in dist Corollary countable set deﬁned deﬁnition denote disjoint equation equivalent example Exercise exists ﬁnite ﬁrst ﬁxed function f fXng given Hence HINT hypothesis identically distributed r.v.’s implies independent r.v.’s inequality inﬁnitely divisible interval large numbers law of large Lebesgue Lebesgue measure left member lemma Let f lim n!1 Markov process Markov property martingale measurable function notation null set obtain optional r.v. permutable probability space proof of Theorem Prove random walk real numbers replaced result right member satisﬁed sequence of independent sequence of r.v.’s strictly positive submartingale subsets sufﬁcient supermartingale Suppose term trivial uniformly integrable vague convergence zero