Universitext

Probability Theory

A Comprehensive Course

Authors: Klenke, Achim

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  • Provides a complete introduction to probability theory, including measure theory and scientific applications
  • New updated edition includes concise summaries of each section, as well as outlooks and questions in the text
  • Clearly written to make complicated mathematics accessible
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eBook $59.99
price for USA in USD
  • ISBN 978-3-030-56402-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-030-56401-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this Textbook

This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory.

Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, 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 integrals and stochastic differential equations.
The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts.

This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.

About the authors

Achim Klenke is a professor at the Johannes Gutenberg University in Mainz, Germany. He is known for his work on interacting particle systems, stochastic analysis, and branching processes, in particular for his pioneering work with Leonid Mytnik on infinite rate mutually catalytic branching processes.

Table of contents (26 chapters)

Table of contents (26 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-030-56402-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-030-56401-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Probability Theory
Book Subtitle
A Comprehensive Course
Authors
Series Title
Universitext
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-56402-5
DOI
10.1007/978-3-030-56402-5
Softcover ISBN
978-3-030-56401-8
Series ISSN
0172-5939
Edition Number
3
Number of Pages
XIV, 716
Number of Illustrations
31 b/w illustrations, 24 illustrations in colour
Topics