250157 VO Stochastic Analysis (2021W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

MIXED

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

Details

Language: English

Examination dates

Lecturers

Marcin Lis

Classes (iCal) - next class is marked with N

Wednesday 06.10. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 07.10. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 13.10. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 14.10. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 20.10. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 21.10. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 27.10. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 28.10. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 03.11. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 04.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 10.11. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 11.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.11. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 18.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 24.11. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 25.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 01.12. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 02.12. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 09.12. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.12. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 16.12. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.01. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 13.01. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.01. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 20.01. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.01. 17:15 - 18:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 27.01. 15:00 - 16:30 Seminarraum 10 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

Oral exam at the end of the course.

Minimum requirements and assessment criteria

Examination topics

Reading list

We will loosely follow (the first 4 chapters of) the lecture notes of Nathanael Berestycki:

https://homepage.univie.ac.at/nathanael.berestycki/teach/StoCal/sc3.pdf

Another valuable source is the book

Brownian Motion, Martingales, and Stochastic Calculus by J-F. Le Gall

Association in the course directory

MSTV

Last modified: Th 06.04.2023 00:22