Levy Process
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A Lévy Process is a stochastic process with independent and stationary increments named after Paul Lévy.
- Example(s):
- Counter-Example(s):
- See: Additive Process, Probability Theory, Paul Lévy (Mathematician), Stochastic Process, Random Variable, Random Walk, Wiener Process, Brownian Motion, Poisson Process, Gamma Process, Discontinuous.
References
2021
- (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Lévy_process Retrieved:2021-8-28.
- In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are 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 processes.
- In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are 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.