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19212901 Basismodul: Stochastics II

Summer Term 2022

lecture Prof. Dr. Nicolas Perkowski, exercise joint with Toyomu Matsuda


Time and place

  •  Lecture:  Tuesdays, 10:00 - 12:00h, SR 031, Arnimallee 6, 
                     Thursdays, 08:00 - 10:00h, SR 031, Arnimallee 6 

  • Exercise Session: Montags, 14:00 - 16:00h, SR 031, Arnimallee 6.

  • Final Exam:  Thursdays, 08:00 - 10:00h, lecture hall, Takustr. 9.

Prerequisits: Stochastics I und Analysis I — III.

Assessment

To receive credits fo the course you need to

  • actively participate in the exercise session 
  • work on and successfully solve the weekly exercises 
  • pass the final exam (see above)

If you are an FU student you only need to register for the course via CM (Campus Management).
If you are not an FU student, you are required to register via MyCampus/Whiteboard.

Exercises 

Problem sets will be put online every Monday and can be found under Assignements in Whiteboard. Solutions (in groups of two!) are due by 2pm on Monday of the following week  –  solutions must be submitted in the tutorial or uploaded through the Whiteboard portal.

Course Overview/ Content:

  • Construction of stochastic processes;
  • conditional expectation;
  • martingales in discrete time: convergence, stopping theorems, inequalities;
  • convergence types in stochastics;
  • uniform integrability;
  • Markov chains in discrete and continuous time: recurrence and transience, invariant measures;
  • convergence in distribution of stochatic processes;
  • Brownian motion and invariance principle.

References

  • Klenke: Wahrscheinlichkeitstheorie
  • Durrett: Probability. Theory and Examples.

Further literature will be given during the lecture.

Lecture videos
can be found on the website of Stochastics II from Summer Term 2020.