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＜電子ブック＞
Probability / by A.N. Shiryaev
(Graduate Texts in Mathematics. ISSN:21975612 ; 95)

版	1st ed. 1984.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1984
本文言語	英語
大きさ	XI, 580 p. 1 illus : online resource
冊子体	Probability / A.N. Shiryayev ; translated by R.P. Boas ; : us,: gw
著者標目	*Shiryaev, A.N author SpringerLink (Online service)
件　名	LCSH:Probabilities FREE:Probability Theory
一般注記	I Elementary Probability Theory -- II Mathematical Foundations of Probability Theory -- III Convergence of Probability Measures. Central Limit Theorem -- IV Sequences and Sums of Independent Random Variables -- V Stationary (Strict Sense) Random Sequences and Ergodic Theory -- VI Stationary (Wide Sense) Random Sequences. L2 Theory -- VII Sequences of Random Variables that Form Martingales -- VIII Sequences of Random Variables that Form Markov Chains -- Historical and Bibliographical Notes -- References -- Index of Symbols This textbook is based on a three-semester course of lectures given by the author in recent years in the Mechanics-Mathematics Faculty of Moscow State University and issued, in part, in mimeographed form under the title Probability, Statistics, Stochastic Processes, I, II by the Moscow State University Press. We follow tradition by devoting the first part of the course (roughly one semester) to the elementary theory of probability (Chapter I). This begins with the construction of probabilistic models with finitely many outcomes and introduces such fundamental probabilistic concepts as sample spaces, events, probability, independence, random variables, expectation, corre­ lation, conditional probabilities, and so on. Many probabilistic and statistical regularities are effectively illustrated even by the simplest random walk generated by Bernoulli trials. In this connection we study both classical results (law of large numbers, local and integral De Moivre and Laplace theorems) and more modern results (for example, the arc sine law). The first chapter concludes with a discussion of dependent random vari­ ables generated by martingales and by Markov chains Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4899-0018-0

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