Overview
- provides a detailed and accessible introduction to the subject and to the more research-oriented literature
- presents illustrative examples and images to help readers understand the key ideas
- introduces the parabolic case side by side with the elliptic one and covers some parts of the regularity theory
Part of the book series: SpringerBriefs on PDEs and Data Science (SBPDEDS)
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Table of contents (7 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the author
Mikko Parviainen, Associate Professor at the University of Jyväskylä, received his PhD from Aalto University in 2007. He previously held a position at Aalto University and was a visiting scholar at Institut Mittag-Leffler, Stockholm, as well as a Fulbright scholar at the University of Pittsburgh. His research interests include nonlinear partial differential equations, stochastic game theory and viscosity solutions.
Bibliographic Information
Book Title: Notes on Tug-of-War Games and the p-Laplace Equation
Authors: Mikko Parviainen
Series Title: SpringerBriefs on PDEs and Data Science
DOI: https://doi.org/10.1007/978-981-99-7879-3
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024
Softcover ISBN: 978-981-99-7878-6Published: 23 February 2024
eBook ISBN: 978-981-99-7879-3Published: 22 February 2024
Series ISSN: 2731-7595
Series E-ISSN: 2731-7609
Edition Number: 1
Number of Pages: VIII, 76
Number of Illustrations: 2 b/w illustrations, 7 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Game Theory, Economics, Social and Behav. Sciences, Analysis, Discrete Mathematics