Probability Theory: A Comprehensive Course de Achim Klenke

Probability Theory: A Comprehensive Course: Universitext

Autor Achim Klenke

en Limba Engleză Paperback – 31 oct 2020

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.

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Specificații

ISBN-13: 9783030564018
ISBN-10: 3030564010
Pagini: 716
Ilustrații: XIV, 716 p. 55 illus., 24 illus. in color.
Dimensiuni: 155 x 235 x 42 mm
Greutate: 1.01 kg
Ediția:3rd ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Universitext

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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

Descriere

Descriere de la o altă ediție sau format:
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.

Recenzii

From the reviews:
"The book is indeed comprehensive, consisting of 26 chapters on different topics. … can be well used as a reference book on a wide range of topics. The target audience is researchers and graduate students … . Numerous advanced topics are included, so that the book is more inclusive … . There is more than enough material for a two-semester course here. … the book will primarily be used as a reference book. For that purpose, it is a rich and relatively inexpensive choice." (Miklós Bóna, MathDL, January, 2008)
"This book of over 600 pages gives a self-contained presentation of modern probability theory. It is based on courses on advanced probability given by the author. … Most of the proofs are well detailed. … This book will be helpful for graduate students in mathematics … and for researchers in mathematics or theoretical physics." (Sophie Lemaire, Mathematical Reviews, Issue 2009 f)