Foundations of Random Processes (046868)

  • Instructor: Robert J. Adler
  • Teaching Assistant: Gal Mendelson
  • Time/Place:
    Lectures: Mondays, 14:30-16:30, Meyer 651.
    Tutorials: Mondays, 16:30-17:30, Meyer, 651.
  • Why this course exists: To take students who have been through the basic  undergraduate courses in Probability and Stochastic Processes and introduce them to the rich (and rigorous, at least at the level of the EE interpretation of the word) world of stochastic processes. The course gives an excellent basis for those who want to use stochastic processes in their own research, but do not intend to specialize in Probability, and an excellent preparation for those who will want to take their education further with fully rigorous courses.
  • Syllabus: See the course outline below. You can also go here for the Hebrew syllabus (which doesn’t quite match the way the course is taught nowadays and which, given the predilections of this semester’s lecturer, is even less relevant than is usually the case).
  • Textbooks: The material will come from a variety of sources, the three main ones being Probability, Theory and Examples by Rick Durrett , Probability and Random Processes by Geoffrey Grimmett and David Stirzaker, and a set of lecture notes (in Hebrew) by Adam Shwartz, Moshe Zakai and Ofer Zeitouni.
    There is also a very nice set of notes on the web by Bruce Hajeck, at a level somewhere between our undergraduate course in Random Signals and the current course. It is a nice thing to have a link to.
  • Grade: The final grade will depend on a combination of homework (30%) and a final exam (70%).
  • Final exam:
    Moed A: 12/07/2017
    Moed B: 03/10/2017
  • Prerequisites: Random Signals (044202) or similar, and an interest in (EE level) rigor.


Course Outline
Lecture Topic
1 Survey of course. Probability spaces. Expectation.
2 Convergence of random variables and probability measures.
3 Conditional probability.
4 Random processes. Separability. Continuity.
5 Gaussian processes.
6 Martingales.
7 Brownian motion. Existence and construction.
8 Properties of Brownian motion.
9 Stochastic integration.
10 Ito calculus and stochastic differential equations
11 Radon-Nikodym derivatives, Girsanov formula, hypothesis testing
12 Point processes: Poisson, permanental, determinantal.
13 Spatial processes: Ising model, percolation


Existence and extension of probability measures