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250068 VO Stochastic processes (2020W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

26.1.2021

Tuesday 06.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 07.10. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 13.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 14.10. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 20.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 21.10. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 27.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 28.10. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 03.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 04.11. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 10.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 11.11. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 17.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 18.11. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 24.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 25.11. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 01.12. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 02.12. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 09.12. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 15.12. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 16.12. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 12.01. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 13.01. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 19.01. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 20.01. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 26.01. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 27.01. 13:15 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

A stochastic process is a sequence of random variables describing the evolution of a system changing randomly over time.

In this course we will focus particularly on Markov chains, where the future evolution of the system depends only on its current state, so that it has no "memory". Although this is a very rich class of stochastic processes (with examples arising in a huge number of applications, including physics, biology, engineering, finance and much more...) there is an elegant and powerful theory which can be used to predict its long time behaviour and fluctuations.

We will mainly develop the theory in discrete time and for discrete state spaces. We will then move on to continuous time and discuss the Kolmogorov forward and backward equations, its links with PDEs such as the heat equation (no prior knowledge required) as well as the Poisson process.
Throughout the course, the theory will be illustrated through many examples including the fundamental notion of branching processes and simple random walk. This will allow us to prove Polya's famous theorem: a drunkard moving at random will almost surely return home in two dimension, but not in three and above!

This theory requires very little prior knowledge: essentially, only a working knowledge of expectation and conditional probability on discrete spaces will be assumed, and some notions of linear algebra. In particular, no knowledge of measure theory will be assumed; in fact we view this course as an excellent way of developing a probabilistic intuition which motivates the development of a measure-based theory in further courses (such as Advanced Probability Theory).

Assessment and permitted materials

Written exam on 26.1.2021
Possibility of oral exam thereafter; contact the lectruer directly.

Minimum requirements and assessment criteria

Examination topics

Reading list

Markov chains, by James Norris (Cambridge University Press).

Association in the course directory

MBIP, MSTP

Last modified: We 31.03.2021 11:28