Franklin

A course on tug-of-war games with random noise : introduction and basic constructions / Marta Lewicka.

Author/Creator:
Lewicka, Marta, author.
Publication:
Cham, Switzerland : Springer, [2020]
Series:
Universitext
Universitext, 0172-5939
Format/Description:
Book
ix, 254 pages : illustrations ; 24 cm.
Subjects:
Potential theory (Mathematics).
Probabilities.
Mathematical analysis.
Summary:
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.
Contents:
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.
Notes:
Includes bibliographical references and index.
ISBN:
9783030462086
3030462080
OCLC:
1192519510
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