## Stochastic Processes III

Contents
The course widens and puts into a more general framework, stochastic process theory learnt from Stochastic Processes I and II. Compared to previous courses in Stochastic Processes, more focus will be on mathematical rigour. Topics included are:

• Point process theory, specifically the Poisson process;
• Markov processes in continuous time;
• Brownian motion;
• Various applications, in particular from queueing theory.

Lecturer Daniel Ahlberg

Course literature

Sidney I. Resnick: Adventures in Stochastic Processes (Birkhäuser)

The book is available electronically via the university library here.

Time and date

The preliminary schedule for the lectures is given here.

It is good to read the material from the textbook before each lecture.

Examination

The course will be evaluated through a written exam. Apart from the written exam there will be a number of hand-in assignments throughout the course.

• ### Hand-in assignments

The students are strongly encouraged to work in pairs. Each student will however have to hand-in his/her own solutions. If one does not solve all exercises, then one can still hand in the solutions to the exercises that have been solved.

Deadline for the first hand-in assignment is October 2.

Deadline for the second hand-in assignment is November 20.

• ### Preliminary schedule

The following outline is preliminary, and may be updated as we go along. The listed exercises are mere suggestions and loosely grouped with the appropriate lecture.

Aug 30 - Lecture 1: Sections 4.1-4.2.

Exercises 4.4, 4.10

Sept 6 - Lecture 2: Sections 4.3-4.4, excluding Section 4.3.1.

Exercises 4.2, 4.3, 4.5, 4.7, 4.11, 4.13, 4.22.

Sept 13 - Lecture 3: Section 4.5-4.6.

Exercises 4.8, 4.14, 4.23, 4.26, 4.27, 4.31.

Sept 20 - Lecture 4: Sections 4.7.1-4.9, and part (a) of Proposition 4.10.1.

Exercises 4.9, 4.12, 4.17, 4.42, 4.48.

Sept 27 - Lecture 5: Sections 5.1-5.3, excluding Section 5.3.1.

Exercises 5.8, 5.11, 5.12.

Oct 11 - Lecture 6: Section 5.4.

Exercises 5.15, 5.16, 5.81, 5.82.

Oct 18 - Lecture 7: Section 5.5.

Exercises 5.4, 5.7, 5.10, 5.14, 5.17, 5.19, 5.56.

Nov 1 - Lecture 8: Section 5.7 and 5.9.

Exercises 5.16, 5.22, 5.28, 5.30, 5.34, 5.41, 5.46.

Nov 8 - Lecture 9: Section 5.7.1.

Exercises 5.47, 5.49ab, 5.51a, 5.52, 5.64, 5.67, 5.77, 5.78.

Nov 15 - Class moved!

Nov 16 (13:15-16, room 37) - Lecture 10: Making up for lost time.

Nov 22 - Lecture 11: Sections 6.1-6.2 and 6.4.

Exercises 6.4, 6.7, 6.11.

Nov 29 - Class moved!

Nov 30 (13:15-16, room 14) - Lecture 12: Section 6.3.

Dec 6 - Lecture 13: Sections 6.5-6.7, but no details from Section 6.6.

Exercises 6.3, 6.8, 6.22, 6.24, 6.25.

Dec 13 - Lecture 14: Sections 6.8-6.9.

Exercises 6.30, 6.32.

Dec 20 - Lecture 15: Repetition.

Jan 9 - Written exam.

• ### Old exams

Below you will find some examples of old exams. Note that these exams were not compiled by the current lecturer of the course.