Probability Theory: A Comprehensive Course - Brossura

Klenke, Achim

Brossura

ISBN 10: 1848000472 ISBN 13: 9781848000476

Casa editrice: Springer Verlag, 2010

Riassunto

Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.

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Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms.

This text is a comprehensive course in modern probability theory and its measure-theoretical foundations. Aimed primarily at graduate students and researchers, the book covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as:

• limit theorems for sums of random variables;
• martingales;
• percolation;
• Markov chains and electrical networks;
• construction of stochastic processes;
• Poisson point processes and infinite divisibility;
• large deviation principles and statistical physics;
• Brownian motion; and
• stochastic integral and stochastic differential equations.

The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.

Dettagli dell?edizione

• Editore: Springer Verlag
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1848000472
• ISBN 13: 9781848000476
• Rilegatura: Copertina flessibile
• Numero di pagine: 616
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com