Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

401-3642-00L  Brownian Motion and Stochastic Calculus

SemesterSpring Semester 2018
LecturersW. Werner
Periodicityyearly recurring course
Language of instructionEnglish



Catalogue data

AbstractThis course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.
ObjectiveThis course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.
Lecture notesLecture notes will be distributed in class.
Literature- J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016).
- I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991).
- 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).
- D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006).
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
ExaminersW. Werner
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

No public learning materials available.
Only public learning materials are listed.

Courses

NumberTitleHoursLecturers
401-3642-00 VBrownian Motion and Stochastic Calculus4 hrs
Wed08-10HG G 3 »
Thu10-12HG D 7.2 »
W. Werner
401-3642-00 UBrownian Motion and Stochastic Calculus
Fri 8-9, Fri 9-10 or Fri 12-13 depending on sufficient demand
1 hrs
Fri08-09HG E 21 »
08-09LFW E 13 »
09-10HG E 21 »
09-10LFW E 13 »
12-13HG E 22 »
12-13LFW E 13 »
W. Werner

Groups

No information on groups available.

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
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Quantitative Finance MasterMathematical Methods for FinanceWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation