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Record Nr. |
UNINA9910483899603321 |
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Autore |
Lewicka Marta |
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Titolo |
A Course on Tug-of-War Games with Random Noise [[electronic resource] ] : Introduction and Basic Constructions / / by Marta Lewicka |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
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ISBN |
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Edizione |
[1st ed. 2020.] |
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Descrizione fisica |
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1 online resource (ix, 254 pages) : illustrations |
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Collana |
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Universitext, , 0172-5939 |
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Disciplina |
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Soggetti |
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Potential theory (Mathematics) |
Probabilities |
Mathematical analysis |
Analysis (Mathematics) |
Potential Theory |
Probability Theory and Stochastic Processes |
Analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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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Sommario/riassunto |
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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. |
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