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An Introduction to Probability Theory - Kiyosi Ito

An Introduction to Probability Theory

Paperback Published: 17th December 1984
ISBN: 9780521269605
Number Of Pages: 224

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Professor Ito is one of the most distinguished probability theorists in the world, and in this modern, concise introduction to the subject he explains basic probabilistic concepts rigorously and yet gives at the same time an intuitive understanding of random phenomena.

In the first chapter he considers finite situations, but from an advanced standpoint that enables the transition to greater generality to be achieved the more easily. Chapter 2 deals with probability measures and includes a discussion of the fundamental concepts of probability theory. These concepts are formulated abstractly but without sacrificing intuition. The last chapter is devoted to infinite sums of independent real random variables. Each chapter is divided into sections that end with a set of problems with hints for solution.

This textbook will be particularly valuable to students of mathematics taking courses in probability theory who need a modern introduction to the subject that yet does not allow overemphasis on abstractness to cloud the issues involved.

Prefacep. v
Notation and abbreviationsp. vii
Finite trialsp. 1
Probability spacesp. 1
Real random variables and random vectorsp. 3
Mixing, direct composition, and tree compositionp. 13
Conditional probabilitiesp. 24
Independencep. 27
Independent random variablesp. 32
The law of large numbersp. 35
Probability measuresp. 38
General trials and probability measuresp. 38
The extension theorem of probability measuresp. 46
Direct products of probability measuresp. 53
Standard probability spacesp. 60
One-dimensional distributionsp. 67
Characteristic functionsp. 80
The weak topology in the distributionsp. 97
D-Dimensional distributionsp. 102
Infinite-dimensional distributionsp. 105
Fundamental concepts in probability theoryp. 110
Separable perfect probability measuresp. 110
Events and random variablesp. 114
Decompositions and o-algebrasp. 123
Independencep. 129
Conditional probability measuresp. 136
Properties of conditional probability measuresp. 145
Real random variablesp. 148
Conditional mean operatorsp. 157
Sums of independent random variablesp. 165
General remarksp. 165
Convergent series of independent random variablesp. 170
Central values and dispersionsp. 175
Divergent series of independent random variablesp. 184
Strong law of large numbersp. 186
Central limit theoremsp. 191
The law of iterated logarithmsp. 199
Gauss's theory of errorsp. 206
Poisson's law of rare eventsp. 209
Indexp. 212
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521269605
ISBN-10: 0521269601
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 224
Published: 17th December 1984
Country of Publication: GB
Dimensions (cm): 23.42 x 15.49  x 1.5
Weight (kg): 0.35