MAGIC093: Markov Processes

Course details

A core MAGIC course

Semester

Autumn 2022
Monday, October 3rd to Friday, December 9th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
80

Description

Markov processes in discrete and continuous time will be presented for finite and countable state spaces in discrete time, as well as for some basic processes in continuous time. Standard material will include generators, Dynkinâ's formula, ergodicity, and (strong) Markov and (strong) Feller properties. A bit more advanced material could include coupling and recurrence applied to convergence rates. Some attention will also be paid to the applicability of Markov processes in a variety of fields such as economics, operational research, biology, and physics. Time permitting we will also look at Monte Carlo Markov chain (MCMC) methods as used in, e.g., (Bayesian) statistics. 

Prerequisites

Some basic knowledge about Markov chains is highly desirable. 

Syllabus

1. Stochastic processes. Definitions of a Markov process. 2. Examples: Random Walks. Generators. Chapman-Kolmogorov equations. 3. Dynkin's identity. Stopping times, (strong) Markov property, (strong) Feller processes. 4. Irreducible Markov processes, ergodic theorems, conditions of ergodicity. 5. Coupling method and application to convergence rates. 6. Applications and MCMC.

Lecturer

  • JT

    Professor Jacco Thijssen

    University
    University of York

Bibliography

No bibliography has been specified for this course.

Assessment

The assessment for this course will be released on Monday 9th January 2023 and is due in by Saturday 21st January 2023 at 23:59.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

Only consortium members have access to these files.

Please log in to view course materials.

Lectures

Please log in to view lecture recordings.