# TMA4265 Stochastic Processes (fall 2011)

## Messages

- [15/12] If you want to check the solution sketch for the exam problems you may look here. And if you also need the problem sheet, here it is.

- [08/12] Note: Chapter 11 is not part of the curriculum for the written exam.

- [29/11] The permitted aid items you are allowed to bring to the exam table are the same as before. You will get the stamped yellow A5 sheet at the department office on the 7th floor in Sentralbygg 2. You can fill this sheet (both sides) with your own handwritten notes.

- [22/11] You can find links to old exam problems at the bottom of this page.

- [21/11] For those of you who would like to see a solution to Exercise 5.10 in the textbook, you can find it here.

- [16/11] The results of the semester project are available in the section TA below.

- [15/11] Those of you who marked the semester project report with only your name, please send your student no. to the TA.

- [27/10] Info about handing in your project report is given under TA below.

- [17/10] You may choose to work alone or together with one other student (taking the course) on the semester project. The group of two hands in one report.

- [14/10] The text of the semester project was updated at 12:05.

- [14/10] It's time for the semester project! Here it is. The deadline for handing in your report is 4 pm on Monday, October 31. There will be two TA's available for you during these two weeks. Check their availability under section TA below. Please also check this message board for possible updates on the project (mistakes, misprints etc.). Good luck!

- [28/09] The time for the semester project is approaching. It will be posted on Friday, October 14. You will then have about two weeks to work on it. The deadline for handing in your report is 4 pm on Monday, October 31.

- [15/08] Welcome to the home page of TMA4265 Stochastic processes for the fall semester 2011. We start the lectures on Monday, August 22, in auditorium S4.

## Textbook

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

## Curriculum

- The curriculum are the chapters and sections listed under 'Lectures' below.

## Lecturer

Professor Arvid Næss. Office: 1144, S2. Email: arvidn@math.ntnu.no

## TA

Håkon Toftaker. Office: 1036, S2. Email: toftaker@math.ntnu.no

- [16/11] The results of the semester project are available here.
- It is only available for those of you who have marked the prosject with either student number or candidate number. Those of you who have marked the project with your name only, should send an email to me with your candidate number.

- [27/10] The semester project should be delivered to my mail box on the 7. floor of central building 2. The box is marked Håkon Toftaker.

Office hours during the semester project:

Håkon Toftaker office 1036: Tuesday 18.10.11 at 10-11, Friday 21.10.11 at 14-15, Monday 24.10.11 at 14-15, Friday 28.10.11 at 14-15 Vaclav Slimacek office 1138: Monday 17.10.11 at 14-15, Thursday 20.10.11 at 10-11 Tuesday 25.10.11 at 10-11, Thursday 27.10.11 at 10-11

## Schedule

: Monday 15:15 - 17:00, S4**Lectures**: Tuesday 10:15 - 12:00, R9**Lectures**: Wednesday 13:15 - 14:00, S4**Exercises**: Tuesday, December 13, 2011**Exam**

## Lectures

Date | Topic | Textbook |
---|---|---|

22.08.10 | Conditional expectation. | Chapter 3 |

23.08.10 | Conditional expectation. | Chapter 3 |

29.08.10 | Conditional expectation. Markov chains. | Chapter 3 and Chapter 4: 4.1 |

30.08.10 | Markov chains | Chapter 4: 4.2 |

05.09.10 | Markov chains | Chapter 4: 4.3 |

06.09.10 | Markov chains | Chapter 4: 4.3, 4.4 |

12.09.10 | Markov chains | Chapter 4: 4.4 |

13.09.10 | Markov chains | Chapter 4: 4.5 |

19.09.10 | Markov chains | Chapter 4: 4.5, 4.5.1 |

20.09.10 | Markov chains | Chapter 4: 4.6, 4.7 |

26.09.10 | Markov chains | Chapter 4: 4.7, 4.8 |

27.10.10 | Markov chains | Chapter 4: 4.8 |

03.10.10 | Markov chains | Chapter 4: 4.9 |

04.10.10 | Poisson process | Chapter 5: 5.2, 5.3 |

10.10.10 | Poisson process | Chapter 5: 5.3 |

11.10.10 | Poisson process | Chapter 5: 5.3 |

17.10.10 | Markov chains | Chapter 6: 6.2, 6.3 |

18.10.10 | Markov chains | Chapter 6: 6.3, 6.4 |

24.10.10 | Markov chains | Chapter 6: 6.4, 6.5 |

25.10.10 | Markov chains | Chapter 6: 6.5 |

31.10.10 | Markov chains | Chapter 6: 6.6 |

01.11.10 | Queueing theory | Chapter 8: 8.2, 8.3.1 |

07.11.10 | Queueing theory | Chapter 8: 8.3.2-5 |

08.11.10 | Queueing theory | Chapter 8: 8.4.1, 8.5.1, 8.5.2 |

14.11.10 | Queueing theory | Chapter 8: 8.5.3, 8.6.1 |

15.11.10 | Queueing theory | Chapter 8: 8.6.2, 8.9.1, 8.9.2 |

21.11.10 | Brownian Motion | Chapter 10: 10.1 |

22.11.10 | Brownian Motion | Chapter 10: 10.2, 10.3 |

## Exercises

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

**Exercise 1**- Chapter 3: 3, 8, 21, 24, 49, 54

(session: Wednesday 07.09.11)**Exercise 2**- Chapter 3: 30, 37, 38, 41
- Chapter 4: 1, 2, 3

(session: Wednesday 14.09.11)**Exercise 3**- Chapter 4: 5–7, 14, 16
- 1998 januar: 1

(session: Wednesday 21.09.11)**Exercise 4**- Chapter 4: 18, 20, 25, 32
- 1998 januar: 2
- 1998 august: 1

(session: Wednesday 28.09.11)**Exercise 5**- Chapter 4: 29, 41, 46, 63
- 1998 august: 2
- 2003 mai: 1

(session: Wednesday 05.10.11)**Exercise 6**- Chapter 4: 64, 65 (reference should be to eq. 4.20, not 4.16), 66
- Chapter 11: 1, 4

(session: Wednesday 12.10.11)**Exercise 7**- Chapter 4: 67–68
- 2003 august: 2

(session: Wednesday 02.11.11)**Exercise 8**- Chapter 5: 2, 4, 6, 10, 14

(session: Wednesday 09.11.11)**Exercise 9**- Chapter 5: 34, 42, 60, 62, 75
- Chapter 6: 1-4

(session: Wednesday 16.11.11)**Exercise 10**- Chapter 6: 9, 10, 14, 17

(session: Thursday 23.11.11)**Exercise 11**- Chapter 8: 1, 4, 7, 8 (9 9th ed), 18

(session: Thursday 30.11.11)**Exercise 12**- Chapter 8: 20, 21, 23, 37, 39
- Chapter 10: 1, 2, 5, 9–10