Every infinitely divisible probability distribution corresponds in a natural way to a Lévy process, i.e., a stochastic process { X t : t ≥ 0 } with stationary independent increments (stationary means that for s < t, the probability distribution of X t − X s depends only on t − s ; independent increments means that that difference is independent of the corresponding difference on any interval not overlapping with [ s, t ], and similarly for any finite number of intervals).