401-3601-00L Probability Theory
Semester | Autumn Semester 2021 |
Lecturers | W. Werner |
Periodicity | yearly recurring course |
Language of instruction | English |
Comment | At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office (Link) after having received the credits. |
Courses
Number | Title | Hours | Lecturers | ||||||||||||||||
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401-3601-00 V | Probability Theory | 4 hrs |
| W. Werner | |||||||||||||||
401-3601-00 U | Probability Theory Groups are selected in myStudies. Tue 14-15 or Tue 15-16 starting in the second week of the semester. | 1 hrs |
| W. Werner |
Catalogue data
Abstract | Basics of probability theory and the theory of stochastic processes in discrete time |
Objective | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, series of independent random variables, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson processes, Markov chains (classification and convergence results). |
Content | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson processes, Markov chains (classification and convergence results). |
Lecture notes | will be available in electronic form. |
Literature | R. Durrett, Probability: Theory and examples, Duxbury Press 1996 H. Bauer, Probability Theory, de Gruyter 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 D. Williams, Probability with martingales, Cambridge University Press 1991 |
Performance assessment
Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
ECTS credits | 10 credits |
Examiners | W. Werner |
Type | session examination |
Language of examination | English |
Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
Mode of examination | oral 20 minutes |
Additional information on mode of examination | 20 minutes preparation and 20 minutes exam (one candidate prepares during the 20 minutes oral exam of the previous candidate). |
This information can be updated until the beginning of the semester; information on the examination timetable is binding. |
Learning materials
Main link | Information |
Only public learning materials are listed. |
Groups
401-3601-00 U | Probability Theory | |||||||||
Groups | G-01 |
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G-02 |
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G-03 |
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G-04 |
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Restrictions
There are no additional restrictions for the registration. |