A Course on Tug-of-War Games with Random Noise : Introduction and Basic Constructions. 1st ed. 2020

種類:

電子ブック

責任表示:

by Marta Lewicka

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Lewicka, Marta.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783030462093 [3030462099]    

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.

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