A course on tug-of-war games with random noise : introduction and basic constructions / Marta Lewicka.
- Cham, Switzerland : Springer, 
ix, 254 pages : illustrations ; 24 cm.
- Potential theory (Mathematics).
- 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.
- 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
- Includes bibliographical references and index.
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