03256nam a22005775i 4500 978-981-99-7879-3 DE-He213 20251030111439.0 cr nn 008mamaa 240222s2024 si | s |||| 0|eng d 9789819978793 978-981-99-7879-3 10.1007/978-981-99-7879-3 doi QA274.2-.28 PBT bicssc PBWL bicssc MAT029000 bisacsh PBT thema PBWL thema Parviainen, Mikko. author. aut http://id.loc.gov/vocabulary/relators/aut 71591 Notes on Tug-of-War Games and the p-Laplace Equation [electronic resource] / by Mikko Parviainen. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. VIII, 76 p. 9 illus., 7 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda SpringerBriefs on PDEs and Data Science, 2731-7609 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. Stochastic analysis. 59375 Game theory. Differential equations. Discrete mathematics. Stochastic Analysis. 59375 Game Theory. Differential Equations. Discrete Mathematics. SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819978786 Printed edition: 9789819978809 SpringerBriefs on PDEs and Data Science, 2731-7609 71592 https://doi.org/10.1007/978-981-99-7879-3 ZDB-2-SMA ZDB-2-SXMS 57819 57819