Lévy and Feller Processes and Applications

We provide a self-contained introduction to Lévy processes (i.e. stochastic processes with independent and stationary increments). This class of processes is the simplest class of processes with jumps; they are commonly used in applications in order to model "fat tails" and non-Gaussian behaviour. Our approach includes a foray into stochastic integration w.r.t. point processes and an outlook to the theory of Feller processes.

Useful literature:
1. Breiman: Probability. SIAM. Chapters 1-5, 9.
2. Billingsley: Probability and Measures. Wiley. Chapters 1-6.
3. Durrett: Probability: Theory and Examples.
4. Cambridge University Press, Chapters 1-5 [4] Williams: Probability with Martingales. Cambridge University Press.
5. Moreover, for a first contact with Brownian motion: Schilling, Partzsch: Brownian Motion. De Gruyter, (Chapters 1-4).

Course leader

Lecturer: Prof. Rene Schilling (TU Dresden, Germany)

Coordinator: Prof. Stefan Geiss (University of Jyvaskyla)

Target group

Prerequisites: Measure-theoretic probability, knowledge of discrete martingales, first encounter with stochastic processes (mainly: Poisson process).

The Summer School annually offers courses for advanced master’s students, graduate students, and post-docs in the various fields of science and information technology.

Course aim

The most important aims of the Summer School are to develop post-graduates scientific readiness and to offer students the possibility to study in a modern, scientific environment and to create connections to the international science community. The Summer School offers an excellent pathway to develop international collaboration in post-graduate research.

Credits info

2 EC
Passing: Obligatory attendance at lectures and completing the exercises.

Grading: Pass/fail

Fee info

EUR 0: Participating the Summer School is free of charge, but student have to cover the costs of own travel, accommodation and meals at Jyväskylä.

Scholarships

The 26th Jyväskylä Summer School is not able to grant any Summer School students financial support.