Convergence of Probability Measures (Google eBook)
A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today.
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Review: Convergence of Probability MeasuresUser Review - David - Goodreads
This is a highly technical book, but a wonderful one. The sheer elegance of the theory explained in the book is actually deeply moving. (Kind of like Galois theory) The book's awesomeness is somehow ... Read full review
Analysis apply argument assume Borel o-ﬁeld Borel sets Brownian motion cadlag functions central limit theorem choose compact set condition contains convergence in distribution converges weakly convex countable deﬁned deﬁnition denote dense density distribution function Donskerís theorem equivalent ergodic Example exist ﬁnd ﬁnite ﬁnite-dimensional distributions ﬁnite-dimensional sets ﬁrst ﬁxed hence holds hypothesis implies inequality inﬁmum inﬁnitely integral interval Lebesgue measure Lemma lim sup liminfn limiting distribution Lindeberg-Lťvy linear log log mapping theorem martingale metric space nonnegative open balls open sets permutation points Poisson polygonal positive prime divisors probability measure probability space Prohorovís proof of Theorem prove random element random function random variables random walk relatively compact satisﬁes satisfying Second Edition Section sequence Skorohod topology speciﬁed stationary Statistical subsequence subset Suppose supremum Theorem 3.1 tight uniformly continuous uniformly distributed values variance weak convergence Wiener measure