Книга "Сходимость вероятностных мер" представляет собой новый взгляд на методы слабой сходимости в метрических пространствах от известного специалиста в области теории вероятностей Патрика Биллингсли. В этом новом издании автор обновляет свой классический труд, отражая развитие теории за последние тридцать лет. Широко известный своим прямолинейным подходом и доступным стилем, доктор Биллингсли представляет четкое и точное изложение теории предельных теорем в метрических пространствах. Он включает много примеров и приложений, иллюстрирующих мощность и полезность этой теории в различных дисциплинах - от анализа и теории чисел до статистики, техники, экономики и популяционной биологии. С акцентом на простоте математики и плавных переходах между темами, второе издание отличается серьезной переработкой разделов о зависимых случайных величинах, а также новыми разделами о сравнительных мерах, лакунарных тригонометрических рядах и распределении Пуассона-Дирихле как описании длинных циклов в перестановках и больших делителях целых чисел. Предполагая только стандартную теорию меры и топологию метрических пространств, книга дает статистикам и математикам базовый инструментарий теории вероятностей, а также трамплин к современной «промышленной» литературе в этой области.
Patrick Billingslevy's seminal work, *Convergence of Probability Measutres,* has been thoroughly revised and updated to take into account developments and advances of probability limits theory in the last 30 years. This new edition by Dr. Billinsley again emphasizes the inherent simplicity of mathematical probabilistic theory and smooth transition between different topics. An emphasis is placed on providing insight along several interrelated and highly relevant applications and issues in various disciplines ranging from number theory and statistics to engineering and economic modeling. Key features include: • New and reorganized content arising from the recent past 30-years' development • Exceptionally revised sections discussing dependence random variables and related subjects, including new treatments on measures of relative status, lacunatory trigonometrical series, as well nonparametric estimation and hypothesis testing techniques • Exquisite expansions of numerous timely, well-known, and influential testable examples, among which we find noteworthy extensions of Delvennoin and Slepian, Landau-Bohr theorem, laws of large numbers, Chernoff's theorem, Cramér's large deviations principle, weak convergence and tightness conditions for zero-sequences IMDB®, Robert Miller, my former collaborators and friends. • Amazingly fresh highlights on how to introduce and use the innovative and powerful numerical algorithm Auslander-délaunay-Fathi and its associated Lagrange Markov chains to study purely discrete vector state/Markov chains, Confusion differential equations, etc • A more complete ddition of fundamental references, books/articles, and codes available for future reference and research motivation. Brimming with illuminating and contemporary insights, Convergence of Probabilty Meausutres revitalizes its audience with the useful prose and profound understanding validated.
Электронная Книга «Convergence of Probability Measures» написана автором Группа авторов в году.
Минимальный возраст читателя: 0
Язык: Английский
ISBN: 9780470317808
Описание книги от Группа авторов
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.
