Graduate course: Lévy processes, the Wiener-Hopf factorisation and applications
Graduate course: Lévy processes, the Wiener-Hopf factorisation and applications |
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Students at the taught course centre need to register for courses. To do this, they should e-mail graduate.studies@maths.ox.ac.uk stating which course(s) they wish to attend. When they register, a consent form will be sent back, which indicates their willingness for the lectures to be recorded.
Local students at Bath will need to activate their library cards in order to gain access to the internet studio where the lectures will be held: 3W4.13
Lectures are every week on Thursdays from the 27th January 2011 between 14:00 and 16:00.
- Here is the timetable: click
In principle some latex notes will appear in due course.
The notes from the starboard and any additional material will be posted below:
First week (27th Jan 2011): Lecture 1 (27.01.11)
Second week (3rd Feb 2011): Lecture 2 (27.01.11)
Third week (10th Feb 2011): No lecture
Fourth week (17th Feb 2011): Lecture 3 (17.02.11)
Fifth week (24th Feb 2011): Lecture 4 (24.02.11)
Sixth week (3rd Mar 2011): Lecture 5 (03.03.11)
Seventh week (10th Mar 2011): Lecture 6 (10.03.11)
Eighth week (17th Mar 2011): Lecture 7 (17.03.11)
Nineth week (24th Mar 2011): No lecture
Tenth week (31st Mar 2011): Lecture 8 (31.03.11)
Eleventh week (7th April 2011) Lecture 9 (07.04.11)
Twelfth week (14th April 2011) Lecture 10 (14.04.11) and Slides
Additional links for this lecture:
http://arxiv.org/abs/0912.4743
http://arxiv.org/abs/1004.4671
This course will be split into two parts. Firstly we shall consider the path structure of a general Lévy process, in particular we shall look at the classical Lévy-Ito decomposition. From this we shall consider the special case of spectrally one-sided Lévy processes. From there we shall progress to the classical Wiener-Hopf factorisation and its meaning as a pathwise decomposition. Again, we shall place particular emphasis on the spectrally negative case. From there we shall move to some classical applied probability models and how the Wiener-Hopf factorisation plays a central role.
Assessment will be on the basis of a take-home exam at the end.
The course is based on the following graduate text book below.
