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Probability Theory

By: Vladimir Rotar

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Hardcover | 19 January 1998

At a Glance

Hardcover
432 Pages

Dimensions(cm)
21.59 x 15.24 x 3.18

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This book presents a rigorous exposition of probability theory for a variety of applications. The first part of the book is a self-contained account of the fundamentals. Material suitable for advanced study is then developed from the basic concepts. Emphasis is placed on examples, sound interpretation of results and scope for applications.A distinctive feature of the book is that it discusses modern applications seldom covered in traditional texts. Two cases in point are risk theory (or comparison of distributions) and stochastic optimization. The book also includes some recent developments of probability theory, for example limit theorems for sums of dependent variables, nonlinear and nonclassical limit theorems. Simplified proofs and a unified approach to the exposition of many results are other key features.The book may be used as a textbook for graduate students and advanced undergraduates, and as a work of reference.

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Preface to the English Edition
Introduction
A space of elementary events
Basic Notions	p. 2
Probability distributions on discrete spaces of elementary events	p. 2
Particular classical schemes	p. 7
Independence of events and sequences of trials	p. 12
Conditional probability	p. 17
Random variables	p. 24
Expectation	p. 30
Variance	p. 40
Higher moments and inequalities for deviations	p. 46
The Law of Large Numbers. Limit Theorems for Bernoulli's Scheme	p. 50
The law of large numbers	p. 50
Appendix to Section 8	p. 55
De Moivre - Laplace theorems	p. 60
The Poisson theorem and the simplest flow of events	p. 65
Generating Functions and Random Walks	p. 70
Generating functions (g.f.'s)	p. 70
On random walks	p. 78
Foundations of the Theory	p. 88
Preliminary constructions	p. 88
Probability distributions	p. 93
Random variables	p. 103
Distributions on Finite-Dimensional Spaces	p. 120
Distributions of random variables	p. 120
Distributions of random vectors	p. 135
Some particular distributions on the real line	p. 144
Covariance analysis and multivariate normal distribution	p. 157
Convergence of distributions	p. 163
Comparison of distributions	p. 181
Conditional Distributions	p. 200
Conditional distributions and expectations	p. 201
Conditional expectations with respect to [sigma]-algebras of events	p. 217
Some Kinds of Dependence	p. 226
Conditionally independent and exchangeable random variables	p. 226
Martingales	p. 233
Markov chains	p. 243
Limit Theorems	p. 260
Limit theorems for maxima and minima. Regularly varying functions	p. 261
Characteristic functions and the first limit theorems for sums	p. 273
Characteristic functions, inversion theorems	p. 287
Limit theorems for sums. The case of finite variances	p. 301
Stable distributions	p. 318
Limit theorems for sums. The general case	p. 341
On large deviations	p. 354
Characteristic functions and limit theorems in the multidimensional case	p. 358
Limit theorems for dependent summands	p. 366
Nonlinear limit theorems	p. 382
Almost Sure Behavior of Sums of Random Variables	p. 390
The Borell-Cantelli theorem and the "zero-one" law	p. 390
The strong law of large numbers (SLLN) and the law of the iterated logarithm	p. 394
The law of large numbers and stochastic optimization problems	p. 405
References	p. 412
Table of Contents provided by Blackwell. All Rights Reserved.

Probability Theory

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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