## Stochastic Analysis Common-Guangqu Zheng (WPI)-A mini-course Lévy processes

Mathematics - Lecture/Discussion

Monday, November 4, 2013

4:00 PM-5:00 PM

Stratton Hall

202

ABSTRACT: Lévy process, named after the French Mathematician Lévy, is a stochastic process with stationary independent increments, which can be viewed as the continuous-time analogue of a random walk. In the first part, we will go through three important objects in details, Poisson processes, Brownian motions and Poisson random measures (then Poisson integrals), each of which plays a very important role in the general theory of Lévy processes. It follows from the Lévy-Khintchine's formula and Lévy-Itô's decomposition that one can express a Lévy process X as the sum of three independent Lévy processes X^1, X^2 and X^3, where X^1 is a drifted linear Brownian motion, X^2 is a compound Poisson process having only jumps of size at least 1, X^3 is a pure-jump martingale having only jumps with size less than 1. Also we will see the intimate relationship between Lévy processes and infinitely divisible distributions by the virtue of Lévy-Khintchine's formula. And stable, self-decomposable random variables would be introduced.

Suggested Audiences:
Adult, College

E-mail:
ma-chair@wpi.edu

Last Modified: October 31, 2013 at 9:30 AM

## Stochastic Analysis Common-Guangqu Zheng (WPI)-A mini-course Lévy processes

Mathematics - Lecture/Discussion

Monday, November 4, 2013

4:00 PM-5:00 PM

Stratton Hall

202

ABSTRACT: Lévy process, named after the French Mathematician Lévy, is a stochastic process with stationary independent increments, which can be viewed as the continuous-time analogue of a random walk. In the first part, we will go through three important objects in details, Poisson processes, Brownian motions and Poisson random measures (then Poisson integrals), each of which plays a very important role in the general theory of Lévy processes. It follows from the Lévy-Khintchine's formula and Lévy-Itô's decomposition that one can express a Lévy process X as the sum of three independent Lévy processes X^1, X^2 and X^3, where X^1 is a drifted linear Brownian motion, X^2 is a compound Poisson process having only jumps of size at least 1, X^3 is a pure-jump martingale having only jumps with size less than 1. Also we will see the intimate relationship between Lévy processes and infinitely divisible distributions by the virtue of Lévy-Khintchine's formula. And stable, self-decomposable random variables would be introduced.

Suggested Audiences: Adult, College

E-mail: ma-chair@wpi.edu

Last Modified: October 31, 2013 at 9:30 AM