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

Record Type:	Electronic resources : Monograph/item
Title/Author:	Notes on tug-of-war games and the p-Laplace equation/ by Mikko Parviainen.
Author:	Parviainen, Mikko.
Published:	Singapore :Springer Nature Singapore : : 2024.,
Description:	viii, 76 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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
Subject:	Harmonic functions. -
Online resource:	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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245 1 0 $a Notes on tug-of-war games and the p-Laplace equation $h [electronic resource] / $c by Mikko Parviainen.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2024.
300 $a viii, 76 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a SpringerBriefs on PDEs and data science, $x 2731-7609
505 0 $a 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.
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.
650 0 $a Harmonic functions. $3 596179
650 0 $a Stochastic processes. $3 520663
650 1 4 $a Stochastic Analysis. $3 3599427
650 2 4 $a Game Theory. $3 2179327
650 2 4 $a Differential Equations. $3 907890
650 2 4 $a Discrete Mathematics. $3 1569938
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs on PDEs and data science. $3 3632373
856 4 0 $u https://doi.org/10.1007/978-981-99-7879-3
950 $a Mathematics and Statistics (SpringerNature-11649)