Probability: A Survey of the Mathematical Theory

Передня обкладинка
John Wiley & Sons, 23 серп. 1996 р. - 189 стор.
The brand new edition of this classic text--with more exercises andeasier to use than ever Like the first edition, this new version ofLamperti's classic text succeeds in making this fascinating area ofmathematics accessible to readers who have limited knowledge ofmeasure theory and only some familiarity with elementaryprobability. Streamlined for even greater clarity and with moreexercises to help develop and reinforce skills, Probability isideal for graduate and advanced undergraduate students--both in andout of the classroom. Probability covers:
* Probability spaces, random variables, and other fundamentalconcepts
* Laws of large numbers and random series, including the Law of theIterated Logarithm
* Characteristic functions, limiting distributions for sums andmaxima, and the "Central Limit Problem"
* The Brownian Motion process
 

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Зміст

Foundations 1 Probability Spaces
1
Random Variables and Their Expectations
5
Independence
12
Conditional Expectations and Probabilities
17
When Do Random Variables Exist?
26
Laws of Large Numbers and Random Series 6 The Weak Law of Large Numbers
31
The Weierstrass Approximation Theorem
38
The Strong Law of Large Numbers
41
Convergence of Random Series
52
More on Independence the 01 Law
57
The Law of the Iterated Logarithm
61
Limiting Distributions and the Central Limit Problem 13 Weak Convergence of Measures
71
The Maximum of a Random Sample
78
Characteristic Functions
81
The Central Limit Theorem
94
Stable Distributions
100

The Strong LawContinued
44

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Про автора (1996)

JOHN W. LAMPERTI is Professor of Mathematics at Dartmouth College and the author of Stochastic Processes: A Survey of the Mathematical Theory.

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