ABSTRACT
The goal of this chapter is to introduce the idea of integration with respect to Brownian motion. To give the reader a sense for the integral, we will start by discussing integration with respect to simple random walk. Let X1, X2, . . . be independent random variables, P{Xi = 1} = P{Xi = −1} = 1/2 and let Sn denote the corresponding simple random walk
Sn = X1 + · · ·+Xn. As in Section 5.2, Example 3, we think of Xn as being the result of a game at time n and we can consider possible betting strategies on the games.
