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A Course on Tug-of-War Games with Random Noise

Introduction and Basic Constructions

  • Textbook
  • © 2020

Overview

Authors:
  1. Marta Lewicka

    1. Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

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  • 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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Table of contents (6 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Marta Lewicka
    Pages 1-7

  3. The Linear Case: Random Walk and Harmonic Functions

    • Marta Lewicka
    Pages 9-35

  4. Tug-of-War with Noise: Case p ∈ [2, ∞)

    • Marta Lewicka
    Pages 37-70

  5. Boundary Aware Tug-of-War with Noise: Case p ∈ (2, ∞)

    • Marta Lewicka
    Pages 71-99

  6. Game-Regularity and Convergence: Case p ∈ (2, ∞)

    • Marta Lewicka
    Pages 101-134

  7. Mixed Tug-of-War with Noise: Case p ∈ (1, ∞)

    • Marta Lewicka
    Pages 135-161

  8. Back Matter

    Pages 163-254
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Keywords

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.

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

  • Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

    Marta Lewicka

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

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