A Course on Tug-of-War Games with Random Noise

Introduction and Basic Constructions

Marta Lewicka (Autor)

Buch | Softcover

IX, 254 Seiten

2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-46208-6 (ISBN)

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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.

Marta Lewicka is a Polish mathematician at the University of Pittsburgh, specializing in Mathematical Analysis. Marta obtained her PhD in 2000 from Scuola Internazionale Superiore di Studi Avanzati with a thesis on Hyperbolic Systems of Conservation Laws. She has subsequently worked on Calculus of Variations, Partial Differential Equations, Continuum Mechanics, and Tug-of-War Games in relation to Nonlinear Potential Theory.

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.

"The book is best suited for advanced graduate students and specialists in nonlinear potential theory. The author provides background appendices for probability, Brownian motion and PDEs." (Bill Satzer, MAA Reviews, April 4, 2021)

Erscheinungsdatum	29.06.2020
Reihe/Serie	Universitext
Zusatzinfo	IX, 254 p. 26 illus., 24 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	409 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Discrete Stochastic Processes • games with noise • Game Theory • mean value properties • Nonlinear Potential Theory • p-Laplacian • regularity theory • Tug-of-War games
ISBN-10	3-030-46208-0 / 3030462080
ISBN-13	978-3-030-46208-6 / 9783030462086
Zustand	Neuware