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

Mikko Parviainen (Autor)

Buch | Softcover

76 Seiten

2024 | 2024 ed.
Springer Verlag, Singapore
978-981-99-7878-6 (ISBN)

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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.

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.

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.

Erscheinungsdatum	23.02.2024
Reihe/Serie	SpringerBriefs on PDEs and Data Science
Zusatzinfo	7 Illustrations, color; 2 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Dynamic programming principle • equations in non-divergence form • normalized or game theoretic p-Laplace equation • normalized or game theoretic p-parabolic equation • p-harmonious • regularity of values and solutions to PDEs • Tug-of-War games
ISBN-10	981-99-7878-5 / 9819978785
ISBN-13	978-981-99-7878-6 / 9789819978786
Zustand	Neuware