Topic outline

  • General

    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.

    • 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

      Oct 11 - Lecture 6: Section 5.4

      Oct 18 - Lecture 7: Section 5.5

      Nov 1 - Lecture 8: Section 5.7

      Nov 8 - Lecture 9: Section 5.7

      Nov 15 - Lecture 10: Selected topics from Sections 5.6 and 5.8-5.11

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

      Nov 29 - Lecture 12: Sections 6.5-6.7

      Dec 6 - Lecture 13: Sections 6.8-6.9

      Dec 13 - Lecture 14: Selected topics from Chapter 6

      Dec 20 - Lecture 15: Repetition

      Jan 9 - Written exam