A course on tug-of-war games with random noise : introduction and basic constructions
著者
書誌事項
A course on tug-of-war games with random noise : introduction and basic constructions
（Universitext）
Springer, c2020
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注記
Includes bibliographical references (p. 249-252) and index
内容説明・目次
内容説明
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.
目次
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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