Also, a process {Yt : t ≥ 0} is said to have independent increments if, for all t0 < t1 < . . . < tn, the n random variables Yt1 − Yt0 , Yt2 − Yt1 , ..., Ytn − Ytn−1 are independent. This condition implies that {Yt : t ≥ 0} is Markovian, but not conversely. The increments are further said to be stationary if, for any t > s and h > 0, the distribution of Yt+h− Ys+h is the same as the distributio...

We introduce the multivariate Ornstein-Uhlenbeck process, solve it analytically, and discuss how it generalizes a vast class of continuous-time and discretetime multivariate processes. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its relationship to statistical arbitrage. We illustrate an application to swap co...