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＜E-Book＞
Notes on Tug-of-War Games and the p-Laplace Equation / by Mikko Parviainen
(SpringerBriefs on PDEs and Data Science. ISSN:27317609)

Edition	1st ed. 2024.
Publisher	Singapore : Springer Nature Singapore : Imprint: Springer
Year	2024
Language	English
Size	VIII, 76 p. 9 illus., 7 illus. in color : online resource
Authors	*Parviainen, Mikko author SpringerLink (Online service)
Subjects	LCSH:Stochastic analysis LCSH:Game theory LCSH:Differential equations LCSH:Discrete mathematics FREE:Stochastic Analysis FREE:Game Theory FREE:Differential Equations FREE:Discrete Mathematics
Notes	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 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. Graduate students and advanced undergraduate students with a basic understanding of probability and partial differential equations will find this book useful HTTP:URL=https://doi.org/10.1007/978-981-99-7879-3

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