12 August 2016
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.
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  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).
Lecturer: Prof. Rene Schilling (TU Dresden, Germany)
Coordinator: Prof. Stefan Geiss (University of Jyvaskyla)
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.
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.
Passing: Obligatory attendance at lectures and completing the exercises.
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.
The 26th Jyväskylä Summer School is not able to grant any Summer School students financial support.