Math and science nerds probably know this one! Stochastic is the antonym of deterministic--that is, randomness. An event may be called stochastic by having a random pattern or probability distribution. Stochastic patterns are difficult to predict or analyzed precisely. Stochastic process can be used interchangeably with random process.
Two well known stochastic processes are Brownian motion and the Monte Carlo method. I would link to one of Wikipedia's animations, but they are extremely hard on the eyes!