Probability Theory: A Comprehensive Course - Brossura

Klenke, Achim

Brossura

ISBN 10: 144715360X ISBN 13: 9781447153603

Casa editrice: Springer Nature, 2013

Riassunto

This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including:
 • limit theorems for sums of random variables
• martingales
• percolation
• Markov chains and electrical networks
• construction of stochastic processes
• Poisson point process and infinite divisibility
• large deviation principles and statistical physics
• Brownian motion
• 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 probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.

Su questo libro

Informazioni sull?autore

Achim Klenke is a professor at the Johannes Gutenberg University in Mainz, Germany. 

Dalla quarta di copertina

This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms.
 
To address these concepts, the title 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 process and infinite divisibility
large deviation principles and statistical physics
Brownian motion
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 probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.

Dettagli dell?edizione

• Editore: Springer Nature
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 144715360X
• ISBN 13: 9781447153603
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 638
• Contatto del produttore: non disponibile