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

Introduction and Basic Constructions
Erscheinungsjahr 2020
ISBN: 978-3-030-46209-3
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 254 Seiten, eBook

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Lewicka, Marta

Inhaltsverzeichnis

1 Introduction.- 2 The linear case: random walk and harmonic functions.- 3 Tug-of-War with noise. Case p  ? [2,8).- 4 Boundary aware tug-of-war with noise. Case  p  ? (2,8).- 5 Game-regularity and convergence. Case  p  ? (2,8).- 6 Mixed tug-of-war with noise. Case  p  ? (1,8).- A Background in probability.- B Background in Brownian motion.- C Background in PDEs. D Solutions to selected exercises.- References.- Index.

Über Autor(innen)

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.