When Lévy processes have finite variation. 

Finite and infinite activity processes. 

Lévy-Itô decomposition. 

The simulation of Lévy processes. 

Simulation of Brownian motion and of Poisson processes. 

The general method of simulation for Lévy processes. 

Poisson integrals and compensated Poisson integrals. Definition, properties and examples. 

Discussion of problems related to subordinators and martingales. 

Discussion of exercises. 

Poisson random measures. 

Subordinator processes: definition and properties. 

Characteristic exponent and Laplace exponent of a subordinator. 

Examples of subordinators: Poisson process, Compound Poisson with jumps of positive size, stable subordinators, Gamma subordinator. 

Subordinators and time change in Lévy processes: example. 

Characteristic exponent for different distributions. 

Lévy processes characteristic exponent  and Lévy characteristics triplet. Examples: Brownian motion with drift, Poisson process, Compound Poisson process.