While financial economics is still in its infancy when compared to the mathematical and natural sciences, it has enjoyed a spectacular period of growth over the past three decades, thanks in part to the mathematical machinery that Wiener, Ito, and others pioneered. In this review article, I shall present a survey of some recent research in this exciting area—more specifically, in empirical finance and financial econometrics—including a discussion of the random walk hypothesis, long-term memory in stock market prices, performance evaluation, and the statistical estimation of diffusion processes. It is my hope that such a survey will serve both as a tribute to the amazing reach of Nobert Wiener's research, and as an enticement to those in the "hard" sciences to take on some of the challenges of modern finance.

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