An additive process, in probability theory, is a cadlag, continuous in probability stochastic process with independent increments. An additive process is the generalization of a Lévy process (a Lévy process is an additive process with stationary increments). An example of an additive process that is not a Lévy process is a Brownian motion with a time-dependent drift.[1] The additive process was introduced by Paul Lévy in 1937.[2]
There are applications of the additive process in quantitative finance[3] (this family of processes can capture important features of the implied volatility) and in digital image processing.[4]