What is levy process?

A levy process is a stochastic process that models the evolution of a continuous-time random variable. It is characterized by the probability distribution of the increments of the process over a fixed time interval. Levy processes have several important properties, including independent increments, stationary increments, and the continuity of sample paths with probability 1.

The most famous example of a Levy process is the Brownian motion, which models the random movement of particles in a fluid. Other examples of Levy processes include the Poisson process, which models the arrival of events in time, and the compound Poisson process, which is used to model the sum of a random number of independent random variables.

Levy processes are widely used in finance to model the behavior of prices, returns, and other financial variables. They are particularly useful for modeling extreme events, such as market crashes or other unexpected events that can have a significant impact on financial markets. Levy processes are also used in physics, biology, and other fields to model random processes where jumps or sudden changes in behavior are important.