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

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.

“This book is very carefully and concisely written. It could be an important source for graduate students as well as for established researchers wanting to increase their knowledge about the interplay of stochastic analysis and nonlinear partial differential equations.” (Marie-Françoise Bidaut-Véron, zbMATH 1555.60003, 2025) “This is a nice monograph on the recently well-investigated topic of tug-of-war games and the p-Laplace equation. ... This well-written monograph, which may be accessible to a broad range of researchers ... .” (Naoyuki Ishimura, Mathematical Reviews, April, 2025)

• 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.