19212901 Basismodul: Stochastics II
Summer Term 2022
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: Thursday, July 21st, 08:00 - 10:00h, lecture hall, Takustr. 9.
- Follow-up Exam: Tuesday, October 4th, 10:00 - 12:00h,
lecture hall B (room B.004), Arnimallee 22.
Prerequisits: Stochastics I und Analysis I — III.
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)
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.
- Klenke: Wahrscheinlichkeitstheorie
- Durrett: Probability. Theory and Examples.
Further literature will be given during the lecture.
can be found on the website of Stochastics II from Summer Term 2020.