550.426 Introduction to Stochastic Processes

550.426 Introduction to Stochastic Processes Spring 2008

Course goal To provide an introduction to several basic classes of stochastic processes, including Poisson processes, renewal processes, Markov chains in both discrete and continuous time, martingales, and Brownian motion. The course is an introduction to the theory and application of stochastic processes. It will be taught at the senior undergraduate level, assuming a knowledge of calculus, linear algebra, and intermediate probability.
Required background Probability at the level of 550.420. Real analysis at the level of 110.405 is helpful but is not required.

Instructor Prof. Jim Fill, 306-F Whitehead Hall, (410) 516-7219, <jimfill@jhu.edu>

Office hours M W 5:45-6:35, or by appointment

Teaching Assistant Takehiko ("Také") Nakama, 212-B Whitehead Hall; office hours: F 2:20 - 4:20 in 212 Whitehead Hall; <nakama@ams.jhu.edu>

Textbook S. Ross. Stochastic Processes, 2nd edition. New York: Wiley, 1996.

Classes, conf. sess. Lectures will be held M W 4:30 - 5:45 in 304 Whitehead Hall. Required conference session (led by Také Nakama) will be held F 1:30 - 2:20 in 12 New Engineering Building.

Grades Breakdown: weekly homework 20%, first midterm exam 20%, second midterm exam 20%, final exam 40%. Course grade also allows for instructor's discretion.

Homework Homework will generally be due each Monday at the start of class. Exceptions will be noted in class.
You may seek the advice of your peers on homework matters, but you must work through and write up the assignments entirely on your own, after destroying any written record of your discussions. If you have collaborated in any fashion, you must explain fully in writing.

YOU MAY NOT IN ANY WAY ACCESS SOLUTIONS DISTRIBUTED IN ANY OTHER COURSE, PAST OR PRESENT, ON STOCHASTIC PROCESSES!
Your solutions must be written legibly and intelligibly in clear English. Use complete sentences, and organize your thoughts for maximum readability by the TA.
Absolutely no late papers will be accepted.

Course outline (rough)

Introduction: 1 week
Poisson process: 2 weeks
Renewal theory: 2 weeks
Discrete-time Markov chains: 2 weeks
Continuous-time Markov chains: 2 weeks
Martingales: 1 week
Brownian motion: 1 week
Poisson approximation: 1 week

Course related materials Access is restricted to .jhu.edu& .jhsph.edu domains only; if you are off campus, please use the VPN Client to gain access.

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Last modified January 29, 2008 by Jim Fill.

Course goal	To provide an introduction to several basic classes of stochastic processes, including Poisson processes, renewal processes, Markov chains in both discrete and continuous time, martingales, and Brownian motion. The course is an introduction to the theory and application of stochastic processes. It will be taught at the senior undergraduate level, assuming a knowledge of calculus, linear algebra, and intermediate probability.
Required background	Probability at the level of 550.420. Real analysis at the level of 110.405 is helpful but is not required.
Instructor	Prof. Jim Fill, 306-F Whitehead Hall, (410) 516-7219, `<jimfill@jhu.edu>`
Office hours	M W 5:45-6:35, or by appointment
Teaching Assistant	Takehiko ("Také") Nakama, 212-B Whitehead Hall; office hours: F 2:20 - 4:20 in 212 Whitehead Hall; `<nakama@ams.jhu.edu>`
Textbook	S. Ross. Stochastic Processes, 2nd edition. New York: Wiley, 1996.
Classes, conf. sess.	Lectures will be held M W 4:30 - 5:45 in 304 Whitehead Hall. Required conference session (led by Také Nakama) will be held F 1:30 - 2:20 in 12 New Engineering Building.
Grades	Breakdown: weekly homework 20%, first midterm exam 20%, second midterm exam 20%, final exam 40%. Course grade also allows for instructor's discretion.
Homework	Homework will generally be due each Monday at the start of class. Exceptions will be noted in class. You may seek the advice of your peers on homework matters, but you must work through and write up the assignments entirely on your own, after destroying any written record of your discussions. If you have collaborated in any fashion, you must explain fully in writing. YOU MAY NOT IN ANY WAY ACCESS SOLUTIONS DISTRIBUTED IN ANY OTHER COURSE, PAST OR PRESENT, ON STOCHASTIC PROCESSES! Your solutions must be written legibly and intelligibly in clear English. Use complete sentences, and organize your thoughts for maximum readability by the TA. Absolutely no late papers will be accepted.
Course outline (rough)	Introduction: 1 week Poisson process: 2 weeks Renewal theory: 2 weeks Discrete-time Markov chains: 2 weeks Continuous-time Markov chains: 2 weeks Martingales: 1 week Brownian motion: 1 week Poisson approximation: 1 week
Course related materials	Access is restricted to .jhu.edu& .jhsph.edu domains only; if you are off campus, please use the VPN Client to gain access.