A Course on Tug-of-War Games with Random Noise: Introduction and Basic Constructions
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.

1136717320
A Course on Tug-of-War Games with Random Noise: Introduction and Basic Constructions
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.

64.99 In Stock
A Course on Tug-of-War Games with Random Noise: Introduction and Basic Constructions

A Course on Tug-of-War Games with Random Noise: Introduction and Basic Constructions

by Marta Lewicka
A Course on Tug-of-War Games with Random Noise: Introduction and Basic Constructions

A Course on Tug-of-War Games with Random Noise: Introduction and Basic Constructions

by Marta Lewicka

Overview

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.

Product Details

ISBN-13: 9783030462086
Publisher: Springer International Publishing
Publication date: 06/20/2020
Series: Universitext
Edition description: 1st ed. 2020
Pages: 254
Product dimensions: 6.10(w) x 9.25(h) x (d)

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.

Table of Contents

1 Introduction.- 2 The linear case: random walk and harmonic functions.- 3 Tug-of-War with noise. Case p ∈ [2,∞).- 4 Boundary aware tug-of-war with noise. Case p ∈ (2,∞).- 5 Game-regularity and convergence. Case p ∈ (2,∞).- 6 Mixed tug-of-war with noise. Case p ∈ (1,∞).- A Background in probability.- B Background in Brownian motion.- C Background in PDEs. D Solutions to selected exercises.- References.- Index.
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