401-4601-61L  Lévy Processes

SemesterAutumn Semester 2011
LecturersP. Embrechts
Periodicitynon-recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-4601-61 VLévy Processes2 hrs
Tue13:15-15:00HG G 3 »
P. Embrechts

Catalogue data

AbstractLévy processes as continuous-time analogue of random walks are one of the most basic and fundamental classes of stochastic processes including Brownian motion and Poisson processes. They have many applications in stochastic modeling as for instance in insurance, finance, queuing theory and telecommunication. This course gives a basic introduction into the theory of Lévy processes.
ObjectiveThe aim of this course is to have a basic knowledge of Lévy processes and infinitely divisble distributions. This includes the famous Lévy-Ito decomposition and path properties. In particular, subordinators and stable Lévy processes will be investigated in detail.
Content(1) Lévy processes and infinitely divisible distributions
(2) Lévy-Ito decomposition
(3) Distributional and path properties of Lévy processes
(4) Some special Lévy processes
(5) Subordinators
Lecture notesA script will not be available.
Literature- Applebaum, D. (2004): Lévy Processes and Stochastic Calculus, Cambridge University Press.
- Bertoin, J. (1996): Lévy Processes, Cambridge University Press.
- Kyprianou, A. E. (2006): Introductory Lectures on Fluctuations of Lévy Processes with Applications, Springer Verlag.
- Sato, K. (1999): Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press.
Prerequisites / NoticeThe course will be taught by Dr. Vicky Fasen, RiskLab, D-MATH, HG F 42.1.
Prerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the standard course "Wahrscheinlichkeitstheorie".

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersP. Embrechts
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
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Only public learning materials are listed.

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Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics MasterSelection: Probability Theory, StatisticsWInformation
Quantitative Finance MasterMathematical Methods for FinanceWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation