ENGLISH

Notes on Tug-of-War Games and the p-Laplace Equation

By Mikko Parviainen

Book information

Publisher
Springer Nature Singapore
Year
2024
ISBN
9789819978786, 9789819978793
DOI
10.1007/978-981-99-7879-3
ISSN
2731-7609
Language
english
Format
PDF
Filesize
2 MB (2328663 bytes)
Series
SpringerBriefs on PDEs and Data Science
Edition
1
Pages
76\83
Orientation
yes
Paginated
yes
Scanned
portrait
Time added
2024-02-26 16:49:39
p-LaplacianRandom WalkTug-of-War Games

Description

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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