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＜電子ブック＞
A Course on Tug-of-War Games with Random Noise : Introduction and Basic Constructions / by Marta Lewicka
(Universitext. ISSN:21916675)

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2020
大きさ	IX, 254 p. 26 illus., 24 illus. in color : online resource
著者標目	*Lewicka, Marta author SpringerLink (Online service)
件　名	LCSH:Potential theory (Mathematics) LCSH:Probabilities LCSH:Mathematical analysis FREE:Potential Theory FREE:Probability Theory FREE:Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-46209-3

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