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Notes on tug-of-war games and the p-Laplace equation

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Notes on tug-of-war games and the p-Laplace equation/ by Mikko Parviainen.
作者:	Parviainen, Mikko.
出版者:	Singapore :Springer Nature Singapore : : 2024.,
面頁冊數:	viii, 76 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Harmonic functions. -
電子資源:	https://doi.org/10.1007/978-981-99-7879-3
ISBN:	9789819978793

Notes on tug-of-war games and the p-Laplace equation
Parviainen, Mikko.

Notes on tug-of-war games and the p-Laplace equation[electronic resource] /by Mikko Parviainen. - Singapore :Springer Nature Singapore :2024. - viii, 76 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs on PDEs and data science,2731-7609. - SpringerBriefs on PDEs and data science..

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.

ISBN: 9789819978793

Standard No.: 10.1007/978-981-99-7879-3doiSubjects--Topical Terms:

596179
Harmonic functions.

LC Class. No.: QA405

Dewey Class. No.: 515.53

Notes on tug-of-war games and the p-Laplace equation
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520 $a 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.
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