03081nam 22006135 450 991084186590332120250807145551.0978981997879310.1007/978-981-99-7879-3(CKB)30499957300041(MiAaPQ)EBC31176076(Au-PeEL)EBL31176076(DE-He213)978-981-99-7879-3(OCoLC)1423364726(EXLCZ)993049995730004120240222d2024 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierNotes on Tug-of-War Games and the p-Laplace Equation /by Mikko Parviainen1st ed. 2024.Singapore :Springer Nature Singapore :Imprint: Springer,2024.1 online resource (83 pages)SpringerBriefs on PDEs and Data Science,2731-76099789819978786 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.SpringerBriefs on PDEs and Data Science,2731-7609Stochastic analysisGame theoryDifferential equationsDiscrete mathematicsStochastic AnalysisGame TheoryDifferential EquationsDiscrete MathematicsStochastic analysis.Game theory.Differential equations.Discrete mathematics.Stochastic Analysis.Game Theory.Differential Equations.Discrete Mathematics.519.22Parviainen Mikko1729790MiAaPQMiAaPQMiAaPQ9910841865903321Notes on Tug-of-War Games and the p-Laplace Equation4140066UNINA