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.

29.99 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: 9783030462093
Publisher: Springer-Verlag New York, LLC
Publication date: 06/19/2020
Series: Universitext
Sold by: Barnes & Noble
Format: eBook
File size: 25 MB
Note: This product may take a few minutes to download.

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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