### Stochastic Processes (Summer Semester 2010)

- Lecturer: Prof. Dr. Nicole Bäuerle
- Classes: Lecture (1589), Problem class (1590), Problem class (1591)
- Weekly hours: 4+2+2

**Please note that the English tutorial has been moved to Wednesday 11:30-13:00, Plank-Hörsaal**

The tutorial at 11.30 is held in English, the one at 14.00 in German.

Schedule | ||
---|---|---|

Lecture: | Tuesday 8:00-9:30 | Chemie-Hörsaal II |

Wednesday 8:00-9:30 | Neuer Hörsaal | |

Problem class: | Wednesday 14:00-15:30 | Hörsaal 107 (50.31) |

Problem class: | Wednesday 11:30-13:00 | Plank-Hörsaal |

Lecturers | ||
---|---|---|

Lecturer, Problem classes, Problem classes | Prof. Dr. Nicole Bäuerle | |

Office hours: by appointment. | ||

Room 2.016 Kollegiengebäude Mathematik (20.30) | ||

Email: nicole.baeuerle@kit.edu | ||

Lecturer, Problem classes, Problem classes | Dipl.-Math. oec. Dominik Joos | |

Office hours: | ||

Room Allianz-Gebäude (05.20) | ||

Email: joos@kit.edu |

# Content

In the first part of the lecture we consider Markov chains in discrete- and continuous-time. These kind of processes are often taken as models for the random evolution of systems in various areas like e.g. telecommunication, production planning, biology and physics. The aim is to show some convergence results which describe the long-term behavior of these systems.

In the second part of the lecture we discuss in detail the Brownian motion, in particular its existence, path properties, the reflexion principle and the strong Markov property.

# Prerequisite

Some knowledge of probability theory is required.

# Problem sheets

- Problem sheet 1, (solutions)
- Problem sheet 2, (solutions)
- Problem sheet 3, (solutions)
- Problem sheet 4, (solutions)
- Problem sheet 5, (solutions)
- Problem sheet 6, (solutions)
- Problem sheet 7, (solutions)
- Problem sheet 8, (solutions)
- Problem sheet 9, (solutions)
- Problem sheet 10, (solutions)
- Problem sheet 11, (solutions)
- Problem sheet 12, (solutions)
- Problem sheet 13, (solutions)

# Examination

Oral exams (English or German) will be held on 28th of June and 15th of September. Registration is possible from 10th June until 16th July at Tatjana Dominic's office (5A-22).