Universität Wien

250152 PS Stochastic Analysis (2021W)

2.00 ECTS (1.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
MIXED
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 07.10. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.10. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.10. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.10. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.11. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.11. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.11. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.11. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.12. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.12. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.12. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.01. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.01. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.01. 13:15 - 14:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course aims at rigorously developing Ito's theory of stochastic calculus and presenting some of its fundamental applications.

Some of the keywords are: Gaussian processes, Brownian motion, conditional expectation, martingales, stopping times, optional stopping, local martingales, stochastic integral, Ito's lemma.

We will first construct Brownian motion and derive its basic properties. Then, we will develop a formal theory of continuous martingales and local martingales, on which we will build the stochastic integral.

Towards the end of the course we will use the constructed theory of stochastic calculus to derive some deep results on the nature of Brownian motion (like for example conformal invariance of two-dimensional Brownian motion).

Familiarity with Advanced Probability will be assumed. However, we will recall the notion of conditional expectation. Elements of complex analysis will be used towards the end of the course.

Assessment and permitted materials

Homework and blackboard presentations

Minimum requirements and assessment criteria

Examination topics

Reading list

Association in the course directory

MSTV

Last modified: We 29.09.2021 11:51