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

Introduction and Basic Constructions
1. Auflage 2020
ISBN: 978-3-030-46208-6
Verlag: Springer International Publishing

Buch, Englisch, 254 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 406 g

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

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

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.