Description
Probability
The Classical Limit Theorems
Author: McKean Henry
A leading authority sheds light on a variety of interesting topics in which probability theory plays a key role.
Language: EnglishSubject for Probability:
Approximative price 45.15 €
In Print (Delivery period: 14 days).
Add to cart the book of McKean Henry
Probability: The Classical Limit Theorems
Publication date: 11-2014
490 p. · 15.2x22.8 cm · Paperback
Publication date: 11-2014
490 p. · 15.2x22.8 cm · Paperback
Approximative price 165.09 €
In Print (Delivery period: 14 days).
Add to cart the book of McKean Henry
Probability: The Classical Limit Theorems
Publication date: 11-2014
488 p. · 15.2x22.9 cm · Hardback
Publication date: 11-2014
488 p. · 15.2x22.9 cm · Hardback
Description
/li>Contents
/li>Biography
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Probability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.
Preface; 1. Preliminaries; 2. Bernoulli trials; 3. The standard random walk; 4. The standard random walk in higher dimensions; 5. LLN, CLT, iterated log, and arcsine in general; 6. Brownian motion; 7. Markov chains; 8. The ergodic theorem; 9. Communication over a noisy channel; 10. Equilibrium statistical mechanics; 11. Statistical mechanics out of equilibrium; 12. Random matrices; Bibliography; Index.
Henry McKean is a professor in the Courant Institute of Mathematical Sciences at New York University. He is a fellow of the American Mathematical Society and in 2007 he received the Leroy P. Steele Prize for his life's work.
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