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

Springer, 2020. — 258 p. — (Universitext). — ISBN: 978-3-030-46208-6.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.The Linear Case: Random Walk and Harmonic Functions
Tug-of-War with Noise: Case p ∈ [2, ∞)
Boundary Aware Tug-of-War with Noise: Case p ∈ (2, ∞)
Game-Regularity and Convergence: Case p ∈ (2, ∞)
Mixed Tug-of-War with Noise: Case p ∈ (1, ∞)