TMA4265 Stochastic Processes (fall 2012)


  • [09/08] Here are suggested solutions to the August exam problems.
  • [04/01/13] Here are suggested solutions to the exam problems.
  • [10/12] The exam is approaching. For your information, the permitted aid items are the same as previous years except for updated list of permitted calculators: HP30S, Citizen SR-270X, Citizen SR-270X College. The list of given formulas is also the same. Check last year's exam sheet. Old exam problems have been linked up at the end of this home page. You are also permitted to bring one stamped, yellow A5 sheet with your own hand written comments (both sides), formulas etc. You get this sheet from the department office at the 7th floor of Sentralbygg 2.
  • [12/11] The results for the semester project are listed here
  • [09/11] While Chapter 11 was relevant for the semester project, it is not part of the curriculum for the written exam in December.
  • [29/10] The exercise session on Thursday (dated 01/10/12) is canceled and instead there is an extra hour (from 18:15 till 20:00) for the next exercise session on next Thursday, 08/10/12.
  • [19/10] In problem 2 you are supposed to estimate the probability distributions of (i), (ii) and (iii) empirically (e.g. histograms) including estimates of mean value and standard deviation . Do not assume a particular distribution, but it would be nice if you made comparisons with suitable, known distributions.
  • [16/10] The deadline for handing in your semester project report is changed to Monday, October 22, 3 pm.
  • [15/10] Sorry, use your candidate no. on the report, not your student no. Your candidate no. for this course is on the StudentWeb.
  • [15/10] PLEASE write your report in English so that the TA can review it. Put your report in Javad's mailbox on the 7th floor and remember to use your student no. as your identifyer (not your name).
  • [12/10] On Tuesday and Thursday next week, there will be project sessions in the computer room Nullrommet (380A). Time: 4-6 pm. The TA will be there to help you.
  • [09/10] On Thursday the exercise session is moved to the computer room Nullrommet (380A). Time: 6-8 pm. The TA is then available to answer (programming) questions for the semester project. If you need access to a computer there and you are from another study program (e.g. indøk), you need to provide your username to '' to get a user account.
  • [05/10] It's time for the semester project! Here it is. The deadline for handing in your report is 3 pm on Friday, October 19. More info on help sessions to be posted later. Please also check this message board for possible updates on the project (mistakes, misprints etc.). Good luck!
  • [04/10] I beg your forgiveness for my absence today! I was totally absorbed in something else and completely forgot about the lectures. I'm truly sorry about this. Fortunately, it is a very rare event :-)
  • [20/09] The exercise session today is cancelled due to illness.
  • [17/09] The semester project will be announced on October 5 with deadline on Friday, October 19 at 15:00. There will be no lectures 15/10 and 18/10. The semester project is an individual project, but if you so desire you may team up with another student.
  • [10/09] NB! The lectures on Thursday are cancelled. But there will be an exercise session. Check for time.
  • [06/09] Sorry about the still missing textbooks. Here is Chap. 4 from the textbook (9. Ed.).
  • [27/08] My good colleague Prof Bo Lindqvist will lecture for you on Thursday
  • [23/08] The lectures for this semester have been posted. Note that this schedule will be changed due to the semester project, which will take place during October. You will then have one week without lectures.
  • [23/08] Some repetition exercises plus Exercise 1 have been posted. Exercise 1 is discussed during the exercise session 30/8.
  • [20/08] Sorry about the missing textbooks. Hopefully they arrive within a week or so. Until then, here are Chap. 2 and Chap. 3 from the textbook (9. Ed.).
  • [13/08] The lectures will start on Monday, August 20, at 08:15 in S1. I am sorry about the somewhat inconvenient lecturing hours. Unfortunately, this aspect of the course is outside our control. But anyway, welcome to one and all!
  • [04/06] Welcome to the home page of TMA 4265 Stochastic Processes. Most likely, the lectures for this course will be in English.


  • Sheldon M. Ross: Introduction to Probability Models, 10th Edition, 2009, Academic Press.


  • The curriculum are the chapters and sections listed under 'Lectures' below. NB! The lectures may be modified as we go along.


Professor Arvid Næss. Office: 1144, Sentralbygg 2. Email:


Javad Rezaie. Office: 1036, Sentralbygg 2. Email:


Studieprog Navn e-post
MTFYMA Emil Gautesen emilga [at] stud [dot] ntnu [dot] no
MTFYMA Hans Olav Hatlem hansoha [at] stud [dot] ntnu [dot] no
MTFYMA Raymond Toft raymont [at] stud [dot] ntnu [dot] no


  • Lectures : Monday 8:15 - 10:00, S1
  • Lectures : Thursday 16:15 - 18:00, S4
  • Exercises: Thursday 18:15 - 19:00, S4
  • Exam: Wednesday, December 19, 2012

Lectures (X = cancelled)

Date Topic Textbook
20.08 Conditional expectation. Chapter 3
23.08 Conditional expectation. Chapter 3
27.08 Conditional expectation. Markov chains. Chapter 3 and Chapter 4: 4.1
30.08 Markov chains Chapter 4: 4.2
03.09 Markov chains Chapter 4: 4.3
06.09 Markov chains Chapter 4: 4.3, 4.4
10.09 Markov chains Chapter 4: 4.4
13.09 X Markov chains Chapter 4:
17.09 Markov chains Chapter 4: 4.4
20.09 Markov chains Chapter 4: 4.4, 4.5.1, 4.6
24.09 Markov chains Chapter 4: 4.7, 4.8
27.09 Markov chains Chapter 4: 4.8
01.10 Markov chains Chapter 4: 4.9
04.10 Poisson process Chapter 4: -
08.10 Poisson process Chapter 4: 4.9
11.10 Poisson process Chapter 5: 5.3
15.10 X Markov chains Chapter : -
18.10 X Markov chains Chapter : -
22.10 Markov chains Chapter 5: 5.3
25.10 Markov chains Chapter 6: 6.2, 6.3
29.10 Markov chains Chapter 6: 6.4, 6.5
01.11 Markov chains Chapter 6: 6.6
05.11 Markov chains Chapter 6: 6.6
08.11 Queueing theory Chapter 8: 8.2, 8.3.1
12.11 Queueing theory Chapter 8: 8.3.2, 8.3.4
15.11 Queueing theory Chapter 8: 8.3.5, 8.5
19.11 Queueing theory Chapter 8: 8.6.1, 8.9.1, 8.9.2
22.11 Brownian Motion Chapter 10.1 - 3

Semester Project

The results for the semester project are listed here


  • Repetition exercise:
    • Chapter 1: 3, 12–13, 18, 36, 39, 44
    • Chapter 2: 12, 43, 64, 74

Old Exam Problems and Solutions

2013-08-09, Arvid Næss