# TMA4265 Stochastic Processes (fall 2010)

## Messages

- [14/12] The solutions to the exam problems have been posted at the bottom of this page.

- [26/11] You may, of course, answer the exam problems in either English or Norwegian. It is your choice.

- [24/11] THE EXAM PROBLEMS ARE WRITTEN IN ENGLISH. IF ANY OF YOU WANT TO HAVE THEM IN NORWEGIAN, PLEASE INFORM ME! IF I DO NOT HEAR FROM YOU, I SHALL ASSUME THAT YOU HAVE ACCEPTED THE ENGLISH VERSION. REMEMBER THAT ANY TRANSLATION RUNS THE RISK OF LOSING PRECISION.

- [24/11] The permitted aids at the exam will be the same as last year. The list of formulas accompanying the exam problems will also be basically the same as last year.

- [23/11] Link to old exam problems with solutions can be found at the bottom of this page. Not all problem sets and solutions are available in English. Sorry about that.

- [22/11] The curriculum are the chapters and sections listed under 'Lectures' below.

- [02/11] Results for the Semester project have been posted bellow. Scores are given on a scale of 0-20. Those who handed in reports with names and not student numbers should contact the TA to get their scores.

- [20/10] The Exercise session 28.10 is canceled due to the TA being away. If you have any questions please drop by the TA's office or email.

- [15/10] The semester project report should be marked with your student number and be placed in the TA's mailbox at the 7'th floor of Sentralbygg 2 by 3:30 pm on Wednesday, October 20. The door to the mail box room is locked after 3:45 pm.

- [06/10] TA hours for the semester project: Monday, October 11, 16:15-18:00 in Room 380a ('Null-rommet') in 'Nordre lavblokk', and Thursday, October 14, 14:15-15:00 in R9. Students who do not have automatic access to Room 380a must send me their name and username. This applies to students outside the Industrial Mathematics Programme. On the project you may work alone or together with one other class mate.

- [06/10] The semester project is now posted. Info on TA hours for this project by tomorrow.

- [22/09] Øvind Bakke will do the lectures on Thursday morning (23/9). The semester project will be posted on Wednesday, October 6. The deadline for submission of your report will be Wednesday, October 20. You may work alone or together with one other person.

- [17/09] NOTE! The exercise session on Thursday 30/9 is canceled due to the TA being out of town. If you have any questions regarding the exercise I (Haakon, the TA) will be available at my office during the following week (week 40), or just send me an email.

- [02/09] NB!!! The lecture on Thursday 9/9, is cancelled. Please, work extra hard on the exercises.

- [01/09] A plan of the lectures will be posted. I shall try to give you this info some time in advance of the lectures to give you an opportunity to prepare for them. A preliminary curriculum will be available soon.

- [19/08] We start the lectures on Monday, August 23, in R9.

- [22/06] Welcome to the home page of TMA4265 Stochastic processes for the fall semester 2010. Information about the start-up of lectures etc. will come later.

## 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

Haakon M. Austad. Office: 1022, S2. Email: haakonmi@math.ntnu.no

## Schedule

: Monday 8:15 - 10:00, R9**Lectures**: Thursday 8:15 - 10:00, S4**Lectures**: Thursday 12:15 - 13, R9**Exercises**: Monday, December 13, 2010**Exam**

## Lectures

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

23.08.10 | Conditional expectation. | Chapter 3 |

26.08.10 | Conditional expectation. | Chapter 3 |

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

02.09.10 | Markov chains | Chapter 4: 4.2 |

06.09.10 | Markov chains | Chapter 4: 4.3 |

09.09.10 | No lecture | — |

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

16.09.10 | Markov chains | Chapter 4: 4.4 |

20.09.10 | Markov chains | Chapter 4: 4.5 |

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

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

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

04.10.10 | Markov chains | Chapter 4: 4.8 |

07.10.10 | Markov chains | Chapter 4: 4.9 |

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

14.10.10 | Poisson process | Chapter 5: 5.3 |

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

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

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

28.10.10 | Markov chains | Chapter 6: 6.5 |

01.11.10 | Markov chains | Chapter 6: 6.6 |

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

08.11.10 | Queueing theory | Chapter 8: 8.3.2, 8.3.3 |

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

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

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

22.11.10 | Brownian Motion | Chapter 10: 10.1 |

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

## Semester Project

Semester project. Deadline for submission is October 20.

- Results:
- 708090: 16
- 696502: 16
- 708101: 16
- 708188: 17
- 697376: 18
- 690688: 11
- 682584: 18
- 684444: 19
- 708185: 19
- 697396: 19
- 708685: 19
- 708684: 19
- 708108: 19
- 708194: 19
- 709483: 19
- 708082: 19
- 669327: 16
- 708956: 16
- 692621: 12
- 692550: 12
- 720206: 15
- 717311: 10
- 697414: 11
- 704828: 11
- 684833: 12
- 708099: 18
- 708087: 18
- 697363: 14
- 717310: 16
- 721063: 16
- 692611: 16
- 708109: 19
- 708832: 19
- 691206: 14
- 708112: 18
- 708092: 18
- 697365: 19
- 697393: 19
- 697421: 19
- 697342: 19
- 708184: 16
- 708182: 16
- 720685: 18
- 720681: 18
- 708102: 19
- 708117: 19
- 708096: 19
- 708084: 19
- 708115: 19
- 708134: 19
- 708131: 20
- 708153: 20
- 708147: 18
- 708179: 18
- 692610: 20
- 692586: 20
- 698965: 4
- 708154: 19
- 705825: 9
- 701692: 16
- 708078: 14
- 684044: 16

## Exercises

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

(session: Thursday 02.09.10)**Exercise 1**- Chapter 3: 3, 8, 21, 24, 49, 54

(session: Thursday 09.09.10)**Exercise 2**- Chapter 3: 30, 37–38, 41
- Chapter 4: 1–3

(session: Thursday 16.09.10)**Exercise 3**- Chapter 4: 5–7, 14, 16
- 1998 januar: 1

(session: Thursday 23.09.10)**Exercise 4**- Chapter 4: 18, 20, 25, 32
- 1998 januar: 2
- 1998 august: 1

(session: Thursday 30.09.10)**Exercise 5**- Chapter 4: 29, 41, 46, 63
- 1998 august: 2
- 2003 mai: 1

(session: Thursday 07.10.10)**Exercise 6**- Chapter 4: 64, 65 (reference should be to eq. 4.20, not 4.16), 66
- Chapter 11: 1, 4

(session: Thursday 28.10.10)**Exercise 7**- Chapter 4: 67–68
- 2003 august: 2

(session: Thursday 04.11.10)**Exercise 8**- Chapter 5: 2, 4, 6, 10, 14

(session: Thursday 11.11.10)**Exercise 9**- Chapter 5: 34, 42, 60, 62, 75
- Chapter 6: 1-4

(session: Thursday 18.11.10)**Exercise 10**- Chapter 6: 9, 10, 14, 17

(session: Thursday 25.11.10)**Exercise 11**- Chapter 8: 1, 4, 7, 9, 18

(session: Thursday 02.12.10)**Exercise 12**- Chapter 8: 20, 21, 23, 37, 39
- Chapter 10: 1, 2, 5, 9–10