: Modeling turbulence, laser cooling, and bursty arrival patterns in communication networks.
: Pricing exotic options and modeling "volatility smiles" where market returns have heavier tails than a normal distribution.
: The statistical properties of an increment depend only on the length of the time interval, not when it occurred. Levy processes and stochastic calculus
The behavior of any Lévy process is entirely determined by its
: Estimating risk and claim sizes in aggregate loss processes. : Modeling turbulence, laser cooling, and bursty arrival
: Used to change probability measures, a vital step in risk-neutral pricing for options. Real-World Applications
: Changes in the process over non-overlapping time intervals do not influence each other. The behavior of any Lévy process is entirely
: Recent research uses Lévy-driven SDEs to improve the performance of non-convex optimization and Bayesian learning algorithms. Lévy Processes and Stochastic Calculus