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Record Nr. |
UNINA9910841865903321 |
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Autore |
Parviainen Mikko |
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Titolo |
Notes on Tug-of-War Games and the p-Laplace Equation / / by Mikko Parviainen |
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Pubbl/distr/stampa |
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Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2024 |
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ISBN |
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Edizione |
[1st ed. 2024.] |
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Descrizione fisica |
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1 online resource (83 pages) |
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Collana |
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SpringerBriefs on PDEs and Data Science, , 2731-7609 |
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Disciplina |
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Soggetti |
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Stochastic analysis |
Game theory |
Differential equations |
Discrete mathematics |
Stochastic Analysis |
Game Theory |
Differential Equations |
Discrete Mathematics |
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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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Chapter 1. Introduction -- Chapter 2. Viscosity Solutions -- Chapter 3. Stochastic Tug-of-War Game -- Chapter 4. Cancellation Method for Regularity of the Tug-of-War with Noise -- Chapter 5. Mean Value Characterizations -- Chapter 6. Further Regularity Methods -- Chapter 7. Open Problems and Comments. |
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Sommario/riassunto |
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This book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since provided new insights and approaches. These lecture notes provide a brief but detailed and accessible introduction to the subject and to the more research-oriented literature. The book also presents the parabolic case side by side with the elliptic case, highlighting the fact that elliptic and parabolic equations are close in spirit in certain aspects. Moreover, it covers some parts of the regularity theory for these problems. |
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