Graduate course: Lévy processes and continuous state branching processes
Graduate course: Lévy processes and continuous state branching processes |
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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.
- Here is the timetable: click
- The lecture on 22nd Oct 2008 10-11am is cancelled all other lectures proceed as timetabled.
I have prepared some latex lecture notes which come in parts and include exercises and they will be posted below. Please note at the end of the course I will update the above three files to take account of typos found during lectures.
The notes from the starboard and any additional material will be posted below:
First week: Lecture 1 (15.10.08), Lecture 2 (16.10.08)
Second week: No Lecture 3 (22.10.08) Lecture 4 (23.10.08)
Third week: Lecture 5 (29.10.08) Lecture 6 (30.10.08)
Fourth week: Lecture 7 (05.11.08) Lecture 8 (06.11.08)
Fifth week: Lecture 9 (12.11.08) Lecture 10 (13.11.08)
Sixth week: Lecture 11 (19.11.08) Lecture 12 (20.11.08)
Seventh week: Lecture 13 (26.11.08) Lecture 14 (27.11.08) Note the last proof I deleted in this lecture was correct!
Eighth week: Lecture 15 (03.12.08) Lecture 16 (04.12.08)
Nineth week: Lecture 17 (10.12.08) Lecture 18 (11.12.08)
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 cases of subordinators and spectrally one-sided Lévy processes. We will discuss some additional properties of these processes in particular the latter. In the second part of the course we will look at a particular application of spectrally one-sided Lévy processes to the theory of continuous state branching processes. In particular we shall see how certain path properties of spectrally negative processes allow us to understand the behaviour of continuous state branching processes. Some key topics are given below.
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.
