Editing Lévy process (section)

{{short description|Stochastic process in probability theory}}
In [[probability theory]], a '''Lévy process''', named after the French mathematician [[Paul Lévy (mathematician)|Paul Lévy]], is a [[stochastic process]]  with independent, stationary increments: it represents the motion of a point whose successive displacements are [[random variable|random]], in which displacements in pairwise disjoint time intervals are independent, and displacements in different time intervals of the same length have identical probability distributions. A Lévy process may thus be viewed as the continuous-time analog of a [[random walk]].

The most well known examples of Lévy processes are the  [[Wiener process]], often called the [[Brownian motion]] process, and the [[Poisson process]]. Further important examples include the [[Gamma process]], the Pascal process, and the Meixner process. Aside from Brownian motion with drift, all other proper (that is, not deterministic) Lévy processes have [[discontinuous]] paths. All Lévy processes are [[additive process]]es.<ref>{{cite book |last1=Sato |first1=Ken-Iti |title=Lévy processes and infinitely divisible distributions |date=1999 |pages=31-68|publisher=Cambridge University Press |isbn=9780521553025}}</ref>