401-3642-00L Brownian Motion and Stochastic Calculus
Semester | Spring Semester 2022 |
Lecturers | M. Schweizer |
Periodicity | yearly recurring course |
Language of instruction | English |
Courses
Number | Title | Hours | Lecturers | ||||||||||
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401-3642-00 V | Brownian Motion and Stochastic Calculus | 4 hrs |
| M. Schweizer | |||||||||
401-3642-00 U | Brownian Motion and Stochastic Calculus Groups are selected in myStudies. | 1 hrs |
| M. Schweizer |
Catalogue data
Abstract | This course gives an introduction to Brownian motion and stochastic calculus. It includes the construction and properties of Brownian motion, basics of Markov processes in continuous time and of Levy processes, and stochastic calculus for continuous semimartingales. |
Objective | This course gives an introduction to Brownian motion and stochastic calculus. The following topics are planned: - Definition and construction of Brownian motion - Some important properties of Brownian motion - Basics of Markov processes in continuous time - Stochastic calculus, including stochastic integration for continuous semimartingales, Ito's formula, Girsanov's theorem, stochastic differential equations and connections with partial differential equations - Basics of Levy processes |
Lecture notes | Lecture notes will be made available in class. |
Literature | - R.F. Bass, Stochastic Processes, Cambidge University Press (2001). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005). - L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000). |
Prerequisites / Notice | Familiarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in - J. Jacod, P. Protter, Probability Essentials, Springer (2004). - R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010). |
Performance assessment
Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
ECTS credits | 10 credits |
Examiners | M. Schweizer |
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 | BMSC course information |
Only public learning materials are listed. |
Groups
401-3642-00 U | Brownian Motion and Stochastic Calculus | ||||||
Groups | G-01 |
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G-02 |
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G-03 |
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Restrictions
There are no additional restrictions for the registration. |