Lévy processes
E1020434
Lévy processes are a class of stochastic processes with stationary, independent increments that generalize random walks and Brownian motion, widely used to model jump-like and continuous-time random phenomena in probability theory and finance.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
class of stochastic processes
ⓘ
mathematical concept ⓘ object of probability theory ⓘ |
| characterizedBy |
Lévy–Itô decomposition
NERFINISHED
ⓘ
Lévy–Khintchine formula NERFINISHED ⓘ |
| definedOn | probability space ⓘ |
| distributionClass | infinitely divisible distributions ⓘ |
| field |
mathematical finance
ⓘ
probability theory ⓘ stochastic processes ⓘ |
| generalizes |
Brownian motion
NERFINISHED
ⓘ
random walks ⓘ |
| hasComponent |
Lévy measure
NERFINISHED
ⓘ
Lévy triplet NERFINISHED ⓘ diffusion coefficient ⓘ drift term ⓘ |
| hasProperty |
Markov property
ⓘ
cadlag paths ⓘ independent increments ⓘ infinitely divisible finite-dimensional distributions ⓘ stationary increments ⓘ stochastic continuity ⓘ |
| includesAsSpecialCase |
Brownian motion
NERFINISHED
ⓘ
Poisson process NERFINISHED ⓘ compound Poisson process ⓘ gamma process ⓘ normal inverse Gaussian process ⓘ stable process ⓘ tempered stable process ⓘ variance gamma process ⓘ |
| indexSet | nonnegative real numbers ⓘ |
| namedAfter | Paul Lévy NERFINISHED ⓘ |
| relatedConcept |
Ornstein–Uhlenbeck processes driven by Lévy noise
ⓘ
infinitely divisible laws ⓘ semimartingales ⓘ subordinators ⓘ |
| timeParameter | continuous time ⓘ |
| usedIn |
biology
ⓘ
insurance mathematics ⓘ option pricing ⓘ physics ⓘ queueing theory ⓘ risk management ⓘ signal processing ⓘ |
| usedToModel |
asset returns with jumps
ⓘ
heavy-tailed phenomena ⓘ jump processes in finance ⓘ random motion with jumps ⓘ turbulence ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.