Statistics 621 - Advanced Stochastic Processes

Section 600, Spring 2010, Prof. D. Cline

Welcome!  This page announces and describes my course for the Spring 2010 semester.  Details may be tentative. 

This is an advanced course in stochastic processes.  Topics may vary from year to year.  They will include both discrete and continuous time processes and possibly point processes.  Martingale theory and Markov theory will play important roles.

Although not completely rigorous, the course will be more mathematical than a first course (such as Statistics 615).  Measure theory is not required, but a few measure theoretic concepts will be introduced as needed.  The intention is to include a layer of theory that would enhance the student's ability to read the literature and to do research.  Homework problems will include both applied and theoretical questions.

For comments or questions, e-mail me (dcline@stat.tamu.edu) or contact the TAMU Statistics Department.

PDF file of this Syllabus

Course Information

Time and Place: TuTh 9:35am-10:50am, Blocker 411.
Instructor: Daren Cline, Blocker 459D, 845-1443.
E-mail: dcline@stat.tamu.edu
Office Hours: MWF 10:00am-11:00am, or by appointment.  (My Schedule)
Course Web Page: http://stat.tamu.edu/~dcline/621.html
Texts: (both are required)
  • G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes, 3rd ed., Oxford Univ. Press.
  • G.R. Grimmett and D.R. Stirzaker, One Thousand Exercises in Probability, Oxford Univ. Press.
References: (to be placed on reserve in Evans Library)
  • R.N. Bhattacharya and E.C. Waymire, Stochastic Processes with Applications, Wiley.
  • E. Çinlar, Introduction to Stochastic Processes, Prentice-Hall.
  • M. Kijima, Markov Processes for Stochastic Modeling, Chapman & Hall.
  • T. Mikosch, Elementary Stochastic Calculus, World Scientific.
  • S.I. Resnick, A Probability Path, Birkhäuser.
  • S.I. Resnick, Adventures in Stochastic Processes, Birkhäuser.
Prerequisite: Statistics 614 or Statistics 615 (or their equivalent).  Measure theory is not required nor is prior experience with stochastic processes as the presentation will mostly be self-contained.  However, this will be a theoretical, Ph.D. level course.  So it is preferable to have had some exposure to advanced probability such as either 614 or 615.
Grading:
  • Homework – 30%.  Please see the homework policy below.
  • Midterm Exam – 30%.  Please see the exam policy below.
  • Final Exam – 40%. 
Course Topics: (tentative; not necessarily in order)
  • Introduction, Conditional Expectation, Stopping Times
  • Countable State Markov Processes, Birth-Death Processes, Queueing Models
  • Martingales
  • Brownian Motion and Diffusion Processes, Ito Integrals
  • Point Processes, Renewal Processes
Disabilities Help: The Americans with Disabilities Act ensures that students with disabilities have reasonable accommodation in their learning environment.  If you have a disability and need help, please contact me and Disability Services in B118 Cain Hall, 845-1637.
Academic Integrity: You are expected to maintain the highest integrity in your work for this class.  This includes not passing off anyone else's work as your own, even with their permission.   Please see the homework and exam policies below for specifics.
Copyright: All the resources I provide for this course are copyrighted and may not be copied or distributed without my express, written permission.

Course Policies
Homework Policy: Your homework solutions must be your own work, not from outside sources, consistent with the university rules on academic integrity.  I expect you to follow this policy scrupulously.  Your performance on the exams is much more likely to be better.
You may use:
  • Your textbook and notes from class.
  • Your notes, homework, etc., from a related class that you took or are taking.
  • References listed on the syllabus.
  • Discussion with me.
  • Voluntary, mutual and cooperative discussion with other students currently taking the class.
You may not use:
  • Solutions manuals (printed or electronic) other than what is provided with the required texts.
  • Solutions from previous classes.
  • Solutions, notes, homework, etc., from classes taught elsewhere or at another time.
  • Solutions, notes, homework, etc., from students who took the class previously.
  • Copying from students in this class, including expecting them to reveal their solutions in "discussion".
Exam Policy: Your exam solutions must be your own work, using only resources I explicitly allow, consistent with the university rules on academic integrity.
Each exam will be comprehensive and cumulative.
  • Please bring your own paper.  I ask that separate problems be on separate sheets. 
  • Bring resources (such as notes) only if I explicitly allow them.
I will not expect you to quote theorems and results explicitly but I do expect you to demonstrate that you can make use of them.  Specifically, you will need to:
  • Show all your work.  This does not necessarily mean showing every individual algebraic or calculus step – but it must be clear what those steps are.
  • Identify (by number, name or description) any theorems, examples or homework problems you use.
  • Clearly identify the solution and/or the end of a proof or derivation.
Missed Work and Incompletes: This is based on university policy.
  • If you must miss an exam due to illness or circumstances beyond your control, notify me or the Statistics Department, in writing or by email (before, if feasible, otherwise within two working days after you return).  See me as soon as possible to schedule a make-up exam.
  • An Incomplete grade will be given only in the event that circumstances beyond your control cause prolonged absence from class and the work cannot be made up.

Course Outline (Tentative)

Topic Textbook Section
1. Introduction  
2. Countable State Markov Processes, Birth-Death Processes, Queueing Models  
3. Martingales and Submartingales, Random Walks  
4. Brownian Motion and Diffusion Processes, Itô Integrals  
5. Point Processes, Poisson Processes  

Lecture Notes

Notes: My lecture notes will be scanned and posted here as I get them ready.
  • Chapter 1.
  • Chapter 2.
  • Chapter 3.
  • Chapter 4.

Assignments

Assignments: Assignments will be posted regularly here.  Please see the homework policy above.  Partial solutions are meant to provide the main ideas, but may not include all necessary details or full justification. They may suggest, however, shortcuts or notational devices that could improve presentation.
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Exam Information

Exams: Information about the exams will be posted here.  Please see the exam policy above.
  • Midterm Exam: TBA.
  • Final Exam: TBA.

Copyright Information

Each document provided on these web pages is copyrighted by me (Daren B.H. Cline) with all rights reserved, whether or not the document explicitly states so.  These documents may only be used for academic purposes and they may not be reproduced or sold without my permission.  That means you may refer to them for other classes or for research, just as you would any book, as long as neither you nor anyone else reproduces them for sale or other distribution.  If you would like to use some of the material for instruction, you need first to get written permission from me (Daren B.H. Cline, TAMU Department of Statistics, College Station TX 77845-3143).