401-3642-00L  Brownian Motion and Stochastic Calculus

SemesterSpring Semester 2022
LecturersM. Schweizer
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-3642-00 VBrownian Motion and Stochastic Calculus4 hrs
Tue08:15-10:00HG E 3 »
Thu08:15-10:00HG E 3 »
M. Schweizer
401-3642-00 UBrownian Motion and Stochastic Calculus
Groups are selected in myStudies.
1 hrs
Fri08:15-09:00HG G 26.5 »
09:15-10:00HG G 26.5 »
12:15-13:00HG G 26.3 »
M. Schweizer

Catalogue data

AbstractThis 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.
ObjectiveThis 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 notesLecture 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 / NoticeFamiliarity 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 credits10 credits
ExaminersM. Schweizer
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
Additional information on mode of examination20 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 linkBMSC course information
Only public learning materials are listed.

Groups

401-3642-00 UBrownian Motion and Stochastic Calculus
GroupsG-01
Fri08:15-09:00HG G 26.5 »
G-02
Fri09:15-10:00HG G 26.5 »
G-03
Fri12:15-13:00HG G 26.3 »

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Computational Biology and Bioinformatics MasterTheoryWInformation
Mathematics BachelorCore Courses: Applied Mathematics and Further Appl.-Oriented FieldsWInformation
Mathematics MasterCore Courses: Applied Mathematics and Further Appl.-Oriented FieldsWInformation
Quantitative Finance MasterMathematical Methods for FinanceWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation
Statistics MasterSubject Specific ElectivesWInformation