Universität Wien
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250157 VO Stochastic Analysis (2023W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Final exam on Wednesday 31.01.2024, 11:30 - 13:00

  • Monday 02.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.10. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.10. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.11. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.11. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.12. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.12. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.12. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.01. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.01. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.01. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.01. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.01. 09:45 - 11:15 Seminarraum 8 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.

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

Assessment and permitted materials

Minimum requirements and assessment criteria

Written examination an the end of the course

Examination topics

Reading list

Brownian Motion and Stochastic Calculus by Karatzas and Shreve;
Brownian Motion, Martingales, and Stochastic Calculus by Le Gall;
Probability with Martingales by Williams.

Association in the course directory

MSTV, MANV

Last modified: Mo 08.04.2024 13:26