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.
