Parviainen, Mikko. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text si 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access VIII, 76 p. 9 illus., 7 illus. in color. online resource. 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. 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. by Mikko Parviainen. Stochastic analysis Game theory Differential equations Discrete mathematics Stochastic Analysis Game Theory Differential Equations Discrete Mathematics QA274.2-.28 9789819978793 https://doi.org/10.1007/978-981-99-7879-3 https://doi.org/10.1007/978-981-99-7879-3 240222 20251030111439.0 978-981-99-7879-3