David Applebaum has a nice survey article on Lévy processes. As we’ve mentioned before, a persistent modelling problem in finance is that the variance of changes in financial time series, such as stock prices, seems to be infinite. This shows up as large jumps in price, larger than can be explained by Brownian motion. Lévy processes, a broad class of stochastic processes that generalize both Brownian motion and Poisson processes, are one candidate to model prices.