Stat 7345 Advanced Probability and Stochastic Processes

MW 900 - 1015 pm in CB3 1.314

Spring 2014

Instructor: Dr. Michael Baron


Syllabus - topics, grading, contact info

eLearning - check your grades and join discussion groups

Text:
Probability by A. N. Shiryaev, 2nd edition, Springer, 1995. ISBN 0-387-94549-0
and other sources, in which case you will receive lecture notes.
Supplementary
texts:
An Introduction to Probability Theory and Its Applications by W. Feller, Vol. 1-2,
3rd edition, Wiley, 1968-1971. ISBN 0471257087, 0471257095.
Options, Futures, and Other Derivatives by J. C. Hull, 8th edition, Prentice Hall, 2012. ISBN 0132777428
Topics:
(1) Advanced Probability. Strong Laws of Large Numbers (4.3). Law of the iterated logarithm (4.4). Glivenko-Cantelli theorem. Infinitely divisible and stable distributions (3.6). Slutsky.s Theorem. Inequalities: Jensen's, Lyapounov's, Hölder's (2.6).
(2) Stochastic processes. Kolmogorov's fundamental theorems (2.9). Markov chains and Markov processes (8). Examples: Binomial process, Poisson process, birth-and-death processes, Brownian motion. Stochastic calculus and Îto formula. Renewal processes and renewal theorem. Martingales (7).
(3) Applications in: finance; genetics; queuing; traffic.

Grading:

Homework 15% Homework will be assigned and briefly checked. A serious and steady
   


effort to work out all the homework problems is highly recommended.

Quizzes 30% Short quizzes closely related to the material of the latest homework
   


assignment. Quizzes are closed-book; one cheat-sheet is allowed.

Midterm exam 20% A 1 1/4-hour midterm is open-book, -notes, etc.
   


Scheduled on March 5, 2014.

Presentations 35% A 25-35 minute presentation of an application of probability and
    stochastic processes. Study materials will be provided. The speaker
    is responsible for distributing neatly typed or written notes (3-5 pages)
    summarizing the presentation. These summaries must contain the main,
    ideas, concepts, methods, and proof plans, but hey cannot consist of
    just the text copied from the study materials. Each presentation will
    be followed by a homework assignment and sometimes even a quiz.

90-100 % = A, 75-90 % = B, 55-75 % = C.