Probability Theory

A Comprehensive Course

Achim Klenke (Autor)

Buch | Softcover

XIV, 716 Seiten

2020 | 3rd ed. 2020
Springer International Publishing (Verlag)
978-3-030-56401-8 (ISBN)

Artikel merken

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.

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.

1 Basic Measure Theory.- 2 Independence.- 3 Generating Functions.- 4 The Integral.- 5 Moments and Laws of Large Numbers.- 6 Convergence Theorems.- 7 L^p-Spaces and the Radon-Nikodym Theorem.- 8 Conditional Expectations.- 9 Martingales.- 10 Optional Sampling Theorems.- 11 Martingale Convergence Theorems and Their Applications.- 12 Backwards Martingales and Exchangeability.- 13 Convergence of Measures.- 14 Probability Measures on Product Spaces.- 15 Characteristic Functions and the Central Limit Theorem.- 16 Infinitely Divisible Distributions.- 17 Markov Chains.- 18 Convergence of Markov Chains.- 19 Markov Chains and Electrical Networks.- 20 Ergodic Theory.- 21 Brownian Motion.- 22 Law of the Iterated Logarithm.- 23 Large Deviations.- 24 The Poisson Point Process.- 25 The Itô Integral.- 26 Stochastic Differential Equations.- References.- Notation Index.- Name Index.- Subject Index.

Erscheinungsdatum	01.11.2020
Reihe/Serie	Universitext
Zusatzinfo	XIV, 716 p. 55 illus., 24 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1104 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Brownian motion • central limit theorem • Integration Theory • Markov Chain • Martingales • measure theory • percolation • Poisson Point Process • Statistical Physics • Stochastic differential equations • Stochastic Integration • Stochastic Processes
ISBN-10	3-030-56401-0 / 3030564010
ISBN-13	978-3-030-56401-8 / 9783030564018
Zustand	Neuware