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Additive process information


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 identically distributed 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]

  1. ^ Tankov & Cont 2003, p. 455.
  2. ^ Tankov & Cont 2003, p. 468.
  3. ^ Tankov & Cont 2003, p. 454.
  4. ^ Bhattacharya & Brockwell 1976, p. 71.

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