- Lecturer
- Vincent Tassion
- Coordinator
- Laurin Köhler-Schindler

Stochastic processes are a way to describe and study the behaviour of systems that evolve in some random way. In this course, the evolution will mostly be with respect to a scalar parameter interpreted as time, so that we discuss the temporal evolution of the system. We introduce several important classes of stochastic processes, analyse their properties and behaviour and show by some examples how they can be used. The main emphasis is on theory; in that sense, "applied" should be understood to mean "applicable".

Outline of the course:

- Discrete-time Markov chains
- Renewal processes
- Poisson point processes
- Standard Poisson processes
- Continuous-time Markov chains

Prerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L).

Lecture notes will be regularly updated.

In addition, here are the slides of the first lecture:

Lectures take place each Tuesday from 10:15 to 13:00 in NO C 60. Exercise classes take place on Wednesdays or Thursdays as indicated below. The enrolment takes place via mystudies.

If you have any questions related to the content of the lectures or the exercises, you are very welcome to ask them on the forum.

The new exercises will be posted here every week on Tuesday. We recommend to look at the problems and try to solve the quiz before the exercise classes on Wednesday or Thursday.

Exercise sheet | Due by | Solutions |
---|---|---|

Exercise sheet 1 | February 28 | Solution 1 |

Exercise sheet 2 | March 7 | Solution 2 |

Exercise sheet 3 | March 14 | Solution 3 |

Exercise sheet 4 | March 21 | Solution 4 |

Exercise sheet 5 | March 28 | Solution 5 |

Exercise sheet 6 | April 4 | Solution 6 |

Exercise sheet 7 | April 18 | Solution 7 |

Exercise sheet 8 | April 25 | Solution 8 |

Exercise sheet 9 | May 2 | Solution 9 |

Exercise sheet 10 | May 9 | Solution 10 |

Exercise sheet 11 | May 16 | Solution 11 |

Exercise sheet 12 | May 23 | Solution 12 |

Exercise sheet 13 | May 30 | Solution 13 |

Exercise sheet 14 | No submission | Solution 14 |

You are welcome to submit your solutions, even though it is not oligatory. In case you decide to submit your solutions, please submit them as a hard copy right before the beginning of the lecture (i.e. before 10:15 on the corresponding due date. Your solutions will then be corrected and returned during the exercise classes or the next lecture.

** First exercise class: ** Wednesday, February 22, or Thursday, February 23

** Time and location:**

Time | Location | Assistant |
---|---|---|

Wednesday, 13:15-14:00 | ML H 41.1 | Laurin Köhler-Schindler |

Thursday, 12:15-13:00 | HG G 26.5 | Ritvik Radhakrishnan |

- R. N. Bhattacharya and E. C. Waymire, "Stochastic Processes with Applications", SIAM (2009), available online.
- R. Durrett, "Essentials of Stochastic Processes", Springer (2016), available online.
- M. Lefebvre, "Applied Stochastic Processes", Springer (2007), available online.
- S. I. Resnick, "Adventures in Stochastic Processes", Birkhäuser (2005).
- G. Last, M. Penrose, "Lectures on the Poisson Process", Cambridge University Press (2017), available online.