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140122  eng 
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a 9781489900180

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1 

a Shiryaev, A.N.

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a Probability
h Elektronische Ressource
c by A.N. Shiryaev

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a 1st ed. 1984

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a New York, NY
b Springer New York
c 1984, 1984

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a XI, 580 p. 1 illus
b online resource

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a 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

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a Probability Theory

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a Probabilities

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7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Graduate Texts in Mathematics

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a 10.1007/9781489900180

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u https://doi.org/10.1007/9781489900180?nosfx=y
x Verlag
3 Volltext

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a 519.2

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a This textbook is based on a threesemester course of lectures given by the author in recent years in the MechanicsMathematics 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
