MM513: Probability theory II (5 ECTS)

STADS: 13001301

Level
Bachelor course

Teaching period

Third quarter (Elective for Scient. students).
Third quarter on third academic year (Compulsory for Mat.Øk. students).

Teacher responsible
No responsible teachers found, contact the department if necessary

Timetable
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Comment:
Ansvarlig lærer: Magdalena Musat, postdoc Tel: 6550 2316 email: musat@imada.sdu.dk

Prerequisites:
None

Academic preconditions:
The students must be familiar with the contents of the courses "Measure- and integration theory" and "Probability theory".

Course introduction
To give the students a solid introduction to the basic theory of stochastic processes in discrete time with special focus on martingales.

Qualifications
The theory for stochastic processes plays an important role in probability theory and its applications in statistics, mathematical finance, functional analysis, etc. The theory of martingales, in particularly, plays a crucial role in the development of stochastic integration as the main tool for solving stochastic differential equations. Having completed the course successfully, the students can be expected to • be familiar with the main types of convergence for stochastic processes in discrete time. • have a solid understanding of the theory of martingales and its applications e.g. to mathematical finance. • be prepared for advanced studies in stochastic differential equations, mathematical finance, statistics and functional analysis.

Expected learning outcome


Subject overview
1. The main types of convergence for stochastic processes in discrete time and their mutual relative strength.
2. The Borel-Cantelli lemma and applications thereof.
3. Existence and uniqueness of conditional expectation for integrable random variables.
4. Martingales, stopping times and optional sampling.
5. The martingale convergence theorem.
6. The strong law of large numbers.
7. Uniformly integrable martingales.


Literature
There isn't any litterature for the course at the moment.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
(a) A number of mandatory assignments during the course. These assignments must be passed in order to be enrolled for the exam.
(b) A 30 minutes oral exam. External examiner, grades according to the 13-point marking scale.

Expected working hours
The teaching method is based on three phase model.

(a) Forelæsninger (25 timer).
(b) Eksaminatorier (25 timer).
Educational activities

Language
No recorded information about the language used in the course.

Course enrollment
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Tuition fees for single courses
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