This advanced lecture (Vertiefungsvorlesung) addresses Master students in Computer Science, Mathematics, Bioinformatics, CuK or Computerlinguistics.


The aim of this course is to expose participants to Stochastic Hybrid Systems. Theoretical results will be illustrated and motivated by applications in different important fields.

Stochastic hybrid systems are systems that combine continuous dynamics with discrete/logic components and are affected by uncertainty. From a theoretical point of view, the study of this class of systems is particularly challenging because they exhibit the complexities that arise from the interaction of

discrete-event systems,

continuous dynamics, and

stochastic processes, either affecting the discrete-event

system transitions or entering the continuous dynamics.


Emphasis will be placed on theoretical advances for this complex and diverse class of systems, in particular on

stochastic hybrid modeling

compositional specification

reachability analysis

model checking

hybrid observer design


Motivation for the theoretical results will be provided by a number of key applications:

air traffic management

automotive systems

communication networks

mathematical finance


The module is offered March 12-23, 2007 as a block course. We usually start at 9:00 in the morning, with about 2 hrs of lecture in the morning, and exercise sessions on some of the afternoons.


Further details will become available here and at the CMS.

  Topic   Date   Instructor   Notes 
0.   Introduction; Timed Automata  12-03-2007  Holger Hermanns 
1.  Measure theory, Probabilities, Stochastic Processes   12-03-2007  Holger Hermanns 
2.   Discrete time Markov Chains  13-03-2007   Holger Hermanns 
3.   Continuous time Markov Chains  14-03-2007  Holger Hermanns 
4.  Markov jump processes; Piecewise Deterministic Markov Processes 15-03-2007   Manuela Bujorianu 
5.  Brownian Motion, Wiener Processes  16-03-2007   Manuela Bujorianu 
6.  Ordinary Differential Equations, Hybrid Systems  19-03-2007 Holger Hermanns 
7.  Applications of Hybrid Systems and Stochastic Processes  20-03-2007  Holger Hermanns 
8.  Stochastic Differential Equations, Diffusion Processes  21-03-2007  Manuela Bujorianu 
9.   Stochastic Hybrid Systems  22-03-2007  Manuela Bujorianu 
10.   Applications of Stochastic Hybrid Systems  23-03-2007   Manuela Bujorianu 

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Prof. Dr.-Ing. Holger Hermanns
Dr. Manuela L. Bujorianu