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
- 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.
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.
- Verlag: Springer / Springer International Publishing / Springer, Berlin
- Artikelnr. des Verlages: 978-3-030-56401-8
- 3. Aufl.
- Seitenzahl: 732
- Erscheinungstermin: 31. Oktober 2020
- Abmessung: 235mm x 155mm x 38mm
- Gewicht: 1084g
- ISBN-13: 9783030564018
- ISBN-10: 3030564010
- Artikelnr.: 59800242
"The book is dedicated to graduate students who start to learn probability theory as well as to those who need an excellent reference book. ... All results are presented in a self-contained way and are rigorously proved. Each section of the 26 chapters ends with a number of exercises, overall more than 270. ... Altogether it is a very valuable book for all students who specialize in probability theory or statistics." (Mathias Trabs, zbMATH, Vol. 1295, 2014)
"The book under review is a standard graduate textbook in this area of mathematics that collects various classical and modern topics in a friendly volume. ... the book contains many exercises. It is a very good source for a course in probability theory for advanced undergraduates and first-year graduate students. ... the book should be useful for a wide range of audiences, including students, instructors, and researchers from all branches of science who are dealing with random phenomena." (Mehdi Hassani, MAA Reviews, May, 2014)