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16WS Stochastische Prozesse

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Welcome! Here you find information and material for my course Stochastic Processes during the winter term 2016/2017.

Please register for the lecture, tutorials, and exercise groups in Porta.




General Information

In this course we investigate Stochastic Processes in general, as well as Brownian motion, martingales, and Markov processes in particular. There are two lectures per week on
  • Tuesday at 10.15 in P2
  • Thursday at 12.15 in HS9
and an associated tutorial on
  • Tuesday at 12.15 in HS1.
As a prerequisite, you are expected to be familiar with
(a) Measure and Integration (e.g., as in the BSc course Maß- und Integrationstheorie).
(b) Probability Theory (e.g., as in the BSc course Wahrscheinlichkeitstheorie).

Within the Stochastic Processes and Mathematical Finance curriculum (see here), this is the first advanced course and basic for all further lectures, seminars, etc. in this area. In particular, the lecture Stochastic Analysis and Mathematical Finance, offered in the summer term 2017, will build upon this lecture.




Course Material

All course material, including the current version of the lecture notes, is password protected and available here. I will provide you with the login details in the lecture.

For background on probability theory, please check the lecture notes for my course on Probability Theory. To brush up on your knowledge of measure and integration, you may wish to consult my lecture notes Maß und Integration. Both are available via the link above.


The illustrations below have been shown in the lecture. Download the Matlab code, and run and tweak the simulations yourself!

  • Random Walk

  • White Noise

  • Markov Chain

  • Renewal Process

  • Natural Filtration

  • Finite-Dimensional Distribution

  • Hitting Time

  • Stopped Process

  • Poisson Random Measure

  • Poisson Process

  • Brownian Motion

  • Fractional Brownian Motion

  • Ornstein-Uhlenbeck Process

  • Langevin Process

  • Lévy Construction of Brownian Motion

  • Donsker's Functional Central Limit Theorem

  • Martingale

  • Optional Stopping

  • Law of the Iterated Logarithm

  • Upcrossings

  • Reflection Principle




Tutorials and Exercise Groups


For all information concerning tutorials and exercise groups, please consult this website.




Examinations


There will be oral exams on
  • March 6 and March 7
  • and a re-examination on June 30.
Please register in Porta, and register with Ms. Thieme-Trapp (E129) to get an appointment.