Universität Wien
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250099 VO Advanced probability theory (2014S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 05.03. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 06.03. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.03. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.03. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.03. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.03. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.03. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.04. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.04. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.04. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.04. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.04. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.05. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 08.05. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.05. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.05. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.05. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.05. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.05. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.06. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.06. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.06. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.06. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.06. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.06. 11:15 - 12:55 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.06. 11:15 - 12:55 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The lecture presents the most important results and concepts of the modern probability theory, using the measure-theoretic framework, in the context of infinite sequences of random variables, i.e. stochastic processes in discrete time. It gives an introduction to basic convergence results for such sequences:
- laws of large numbers, central limit theorem, large deviation for independent sequences
- convergence of stochastic series
- martingale convergence theorems
- convergence of Markov chains
We discuss weak convergence of probability measures on function spaces and construct the Brownian motion by means of Donsker's theorem.

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

Knowledge and understanding of the lecture content

Examination topics

Reading list

see http://www.mat.univie.ac.at/~cerny/teaching-SS2014.html

Association in the course directory

MSTW

Last modified: Mo 07.09.2020 15:40