Overview
- Provides a rigorous, self-contained introduction to the emerging field of tug-of-war games
- Includes background and auxiliary material on probability and partial differential equations
- Includes exercises with solutions
Part of the book series: Universitext (UTX)
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About this book
This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise.
The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.
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Keywords
Table of contents (6 chapters)
Reviews
“The book is best suited for advanced graduate students and specialists in nonlinear potential theory. The author provides background appendices for probability, Brownian motion and PDEs.” (Bill Satzer, MAA Reviews, April 4, 2021)
Authors and Affiliations
About the author
Marta Lewicka is a Polish mathematician at the University of Pittsburgh, specializing in Mathematical Analysis. Marta obtained her PhD in 2000 from Scuola Internazionale Superiore di Studi Avanzati with a thesis on Hyperbolic Systems of Conservation Laws. She has subsequently worked on Calculus of Variations, Partial Differential Equations, Continuum Mechanics, and Tug-of-War Games in relation to Nonlinear Potential Theory.
Bibliographic Information
Book Title: A Course on Tug-of-War Games with Random Noise
Book Subtitle: Introduction and Basic Constructions
Authors: Marta Lewicka
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-030-46209-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-46208-6Published: 20 June 2020
eBook ISBN: 978-3-030-46209-3Published: 19 June 2020
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: IX, 254
Number of Illustrations: 2 b/w illustrations, 24 illustrations in colour
Topics: Potential Theory, Probability Theory and Stochastic Processes, Analysis