A Course on Tug-of-War Games with Random Noise
Introduction and Basic Constructions
Authors: Lewicka, Marta
Free Preview- 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
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- About this Textbook
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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.
- About the authors
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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.
- Table of contents (6 chapters)
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Introduction
Pages 1-7
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The Linear Case: Random Walk and Harmonic Functions
Pages 9-35
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Tug-of-War with Noise: Case p ∈ [2, ∞)
Pages 37-70
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Boundary Aware Tug-of-War with Noise: Case p ∈ (2, ∞)
Pages 71-99
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Game-Regularity and Convergence: Case p ∈ (2, ∞)
Pages 101-134
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- A Course on Tug-of-War Games with Random Noise
- Book Subtitle
- Introduction and Basic Constructions
- Authors
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- Marta Lewicka
- 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
- 978-3-030-46209-3
- DOI
- 10.1007/978-3-030-46209-3
- Softcover ISBN
- 978-3-030-46208-6
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- IX, 254
- Number of Illustrations
- 2 b/w illustrations, 24 illustrations in colour
- Topics
