Graduate course: Local times and excursion theory for Markov processes.

The main purpose of this course is to describe the estructure of the succesive lengths of the intervals of excursion of a strong Markov process away from some given point. In this direction, we may define an increasing process called the Local time which stays constant on the excursion interval. Some applications to Brownian motion and Levy processes will be given.

Lecture notes:

• Monotone class theorem.
• Poisson point processes and subordinators.
• Local times for Markov processes.
• Excursion theory for Markov processes.
• Applications.

To be continued in February ...