STOCHASTIC PROCESSES

(098413)

Spring semester, 2004/5

• Instructor: Robert J. Adler
  
• Teaching Assistant: Sreekar Vadlamani
  
• Times:
  Lectures: Mondays, 10:30-12:30, 13:30-14:30, Bloomfield Building (IE&M) Room to be determined
  Exercise class: Mondays: 14:30-15:30, Bloomfield Building (IE&M) Room to be determined
  
• Content: The course will treat basic stochastic process theory at a fairly rigorous mathematical level, although without assuming any measure theory. More details are in the lecture outline below.
  
• Grade: The final grade will be based on a combination of homework (50%) and a 3 hour final examination (50%).
  
• Prerequisites: Students will need basic knowledge of stochastic processes at the level of Stochastic Processes in Operations Research 094314 or equivalent. Some basic analysis, as in Elements of Modern Analysis for Electrical Engineering 108324 is very strongly recommended.
  

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COURSE OUTLINE

The following outline is not cast in stone and will probably change as the semester progresses. Nevertheless, it should give you an idea of where we shall be heading.

The core reference is Probability and Random Processes by Grimmett and Stirzaker, which I shall follow quite closely for nearly all of the semester. I very strongly recommend getting yourself a copy of this.
Many people like Adventures in Stochastic Processes by Sid Resnick, which also has more detailed arguments than does the book by Grimmett and Stirzaker. Its sense of humour will appeal to those of you brought up in American, rather than British, culture.
While they are now rather outdated, A First Course in Stochastic Processes and A Second Course in Stochastic Processes by Karlin and Taylor have lots of good worked examples. Similarly, there is also an older (1975) book Introduction to Stochastic Processes by Erhan Cinlar. While parts of it are out of date, it is hard to find a better or clearer introduction to continuous time Markov processes.
The Technion libraries have multiple (but probably not enough) copies of all the above books.

Weeks	Topic
1	Convergence of random variables, characteristic functions.
2	Laws of large numbers, large deviations,
3	Random walk.
4	Generating functions, branching processes.
5	Discrete time Markov processes, classification of states, stationary distributions.
6	Continuous time Markov processes, semigroups, Poisson processes.
7	Continuous time Markov processes, continued.
8	Stationary processes, autocovariance and spectrum, ergodic theory, Gaussian processes.
9	Discrete time martingales, stopping times.
10	Optional stopping, maximal inequalities.
11	Backward and continuous time martingales.
12	Brownian motion, convergence to Brownian motion.
13	Diffusion processes, first passage times, relation to partial differential equations.
14	Stochastic calculus, Ito integral, Ito's formula.

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ADDITIONAL INFORMATION

If you have any questions, feel free to write to me at robert@ieadler.technion.ac.il. or call me in the office at 8294503.

If you are reading this in hard copy rather than on the web, go to the Teaching section of my homepage at ie.technion.ac.il/Adler.phtml to get the hyperlinks.