Introduction

The fundamental works of Doob, Hunt, Kakutani, Kolmogorov, Lévy, and many others have shown a profound and powerful connection between the classical linear potential theory and the corresponding probability theory. The connection between harmonic functions, the mean value property, and the expected value of a random walk is further illustrated in the examples. Such a connection appears to require linearity, but the approach turns out to be useful in the nonlinear theory as well.