Universitext

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

Introduction and Basic Constructions

Authors: Lewicka, Marta

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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
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eBook $19.99
$54.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-46209-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $29.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-46208-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this Textbook

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

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)

Table of contents (6 chapters)
  • Introduction

    Pages 1-7

    Lewicka, Marta

  • The Linear Case: Random Walk and Harmonic Functions

    Pages 9-35

    Lewicka, Marta

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

    Pages 37-70

    Lewicka, Marta

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

    Pages 71-99

    Lewicka, Marta

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

    Pages 101-134

    Lewicka, Marta

Buy this book

eBook $19.99
$54.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-46209-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $29.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-46208-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
A Course on Tug-of-War Games with Random Noise
Book Subtitle
Introduction and Basic Constructions
Authors
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