Universität Wien
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250189 VO Advanced probability theory (2021S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 04.03. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 11.03. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 18.03. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 25.03. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 15.04. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 22.04. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 29.04. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 06.05. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 20.05. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 27.05. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 10.06. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 17.06. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 24.06. 08:00 - 11:15 Digital
    Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

The course starts by a definition of a probability space and spans crucial aspects of Probability Theory, including the expectation and the variance of a random variable, the law of large numbers and the central limit theorem, martingales and stopping times, finishing at Doob's martingale convergence theorem. The course also covers the required parts of Measure Theory.

The main topics:
- random variables, expectation, independence
- Borel-Cantelli lemmas, Kolmogorov zero-one law
- law of large numbers
- weak convergence
- central limit theorem
- martingales

An additional chapter of the course (not required for the exam) is an introduction to the percolation theory (https://en.wikipedia.org/wiki/Percolation_theory):
- classical theorems about the phase transition
- brief overview of recent progress (two Fields Medals, multiple breakthroughs)
- open questions
The aim of this chapter is to give a beautiful example of a probability space and to familiarize the audience with this exciting area of Mathematics.

Assessment and permitted materials

Oral exam (contact the lecturer directly)

Minimum requirements and assessment criteria

The course is in English.
No specific background is assumed.
Intuition coming from basic Probability Theory and Mathematical Analysis would be helpful.

Examination topics

All of the above, excluding percolation

Reading list

Billingsley "Probability and Measure"
https://www.colorado.edu/amath/sites/default/files/attached-files/billingsley.pdf

Association in the course directory

MSTW

Last modified: Fr 12.05.2023 00:21