For the first half of the course, the course will closely follow the course textbook:
Required Text: Sheldon Ross,
Introduction to Probability Models, ninth edition, Academic Press, New York.
(This is a new edition; it came out at the end of 2006.)
The first week (two days, four classes): Chapters 1-3: a review of probability theory.
The next week (two days, four classes): Chapter 4: discrete-time Markov chains (DTMC's).
The next week (two days, four classes): Chapters 5 and 6: the exponential distribution, Poisson process and continuous-time Markov chains (CTMC's).
MIDTERM EXAM: Monday, July 30, on above.
one day (two classes): Chapter 7: renewal processes .
The next week (two days, four classes): martingales and arbitrage. (following Professor Sigman's notes)
The next week (two days, four classes): Chapter 10, Brownian motion and the Black-Scholes formula (and Professor Sigman's notes).
FINAL EXAM: Wednesday, August 22, on all of the above.
