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Room: Think Tank 15, SUTD

Time: Tuesdays and Thursdays, 1:00 pm to 3:00 pm.

Begins: January 27, 2015.

Office hours: By appointment.

Course description:

The aim of this course is to acquaint students with the basic tools for modeling stochastic phenomena. The course will not use measure theory, but theorems will be proved and knowledge of elementary probability and advanced calculus will be assumed.

In particular, after revisiting the main concepts of probability, we will treat the following topics:

  • Markov chains - discrete and continuous time.
  • Poisson processes.
  • Renewal theory.
  • Brownian motions and/or Gaussian processes. (time permitting)

References

  • S. I. Resnick (1992), Adventures in Stochastic Processes, Birkha├╝ser.
    -- I will primarily follow this book.
  • R. Durrett (2012), Essentials of Stochastic Processes, Springer.
  • M. Lefebvre (2007), Applied Stochastic Processes, Springer.
  • S. Ross (1995), Stochastic Processes, Wiley.

Assessment

  • The final score will be calculated as follows: Homework 20%, Midterm 30%, Finals 50%.
  • There will be four/ five homework assignments over the entire period of the lectures. Homework assignments will be uploaded in this webpage with due dates mentioned. Late submissions will not be entertained.

Class notes

Homework

  • Homework 1 due 17th February, 2015 before class.

    Correction in first line of question 5: it should be "offspring" distribution instead of "progeny" distribution.

  • Homework 2 due 5th March, 2015 before class.
  • Homework 3 due 10th April, 2015. (Advice: you don't have to start solving this before the midterm)
  • Homework 4 due 23rd April, 2015 before class
  • Note 1: The homework assignments are provided both for assessment and a little bit of practice. Of course, doing more problems will lead to a better undertanding of the topics. The texts and references have ample exercises, and it is recommended that you try them. ESD grauduate students are especially encouraged here to do more problems, as they will have to appear for a qualifying exam on Stochastic Modeling soon.
  • Note 2: You can slide your homework through my office door (1.702-04). You can also email me your homework, but please do send it as a single pdf file.

Midterm

  • Date: 24th March, 2015.
  • Time: 5:30 pm to 7:30 pm
  • Venue: Think Tank 14
  • Syllabus: Material covered in class until 5th March, 2015.
  • The exam is closed notes.
  • You can bring one A4 sheet of paper with hand-written notes (on both sides) for the exam.
  • No calculators are allowed.

Final Exam

  • Date: 29th April, 2015.
  • Time: 10:00 am to 1:00pm
  • Venue: Think Tank 15
  • Syllabus: Whatever has been taught in class.
  • The exam is closed notes.
  • You can bring one A4 sheet of paper with hand-written notes (on both sides) for the exam.
  • No calculators are allowed.