# PhD course in Point Processes

This is to inform you that Tomas Björk (professor em at Handelshögskolan

and KTH) will give a PhD course on point processes (7.5 hp) at

the department of mathematics at Stockholm university in January-February. More information about the course content can be found below. Do contact Tomas

(Tomas.Bjork@hhs.se) if you have further questions.

**Time:
**
Wed 2018-01-17 10.00 - 15.00

**Lecturer: **
Tomas Björk

**Location: **
Room 31, house 5, SU

The course will be given on Wednesdays at 10-12 and 13-15 in room 31 (house 5), starting January 17. Tomas is an excellent lecturer so I warmly recommend the course for anyone interested in learning more about

this topic! (Mia Deijfen)

## Point Processes in Continuous Time

The object of this course is to give an introduction to the dynamical theory of point processes in continuous time. In particular we will study the deep connections between point processes and martingale theory.

### Contents:

The Poisson Process and the Watanabe martingale characterization of the Poisson process. Counting processes with stochastic intensities. Cox processes (a.k.a. doubly stochastic Poisson processes). Marked point processes. Absolutely continuous changes of measure and the Girsanov Theorem for point processes. Maximum likelihood estimation. Jump diffusions and the corresponding Ito formula. The infinitesimal generator and the connection with PIDE theory, Feynmac-Kac representations, and the Kolmogorov equation. Optimal stochastic control of Markovian jump diffusions.

Time permitting, and depending on the interests of the students, we may also study applications to finance, information theory, queuing theory, insurance, and non-linear filtering theory.

### Prerequisites:

The student needs to be familiar with the elements of abstract probability theory, including basic measure theory. No previous knowledge of point process theory is assumed. If needed there will be a self-contained, hands on, introduction to stochastic calculus (Ito calculus). No previous knowledge of stochastic calculus and/or martingale theory is thus assumed.

### Teacher:

Tomas Björk, Stockholm School of Economics

### Literature:

Lecture notes and OH slides will be made available to the students. For a preview of some of the material, see the notes on point processes at the web page https://www.hhs.se/en/Research/Departments/DF/people/person/?personId=371033

### Schedule:

The lectures will be 10-12 and 13-15 on Wednesdays, starting Wednesday 17 January.