Statistics 615 – Introduction to Stochastic Processes

Section 600, Fall 2008, Prof. D. Cline

Welcome!  This page announces and describes my course for the Fall 2008 semester. 

This course is a non-measure theoretic survey of basic stochastic processes, including countable state space Markov processes, Poisson processes, renewal processes and Brownian motion.  Emphasis is on establishing and using the primary results.  Applied examples and problems are included but this is not an applied stochastic processes course.

Although we do not discuss statistical applications per se, the material is very relevant for modern statistics. In particular, the following areas rely heavily on stochastic processes of one sort or another: time series, Bayesian methods, spatial statistics, longitudinal clinical trials, bioinformatics and functional data analysis.

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

PDF file of this Syllabus

Course Information

Adventures in Stochastic Processes, S.I. Resnick (Birkhäuser).
Time and Place: MWF 3:00–3:50, Blocker 411
Instructor: Daren Cline, Blocker 459D, 845-1443.
E-mail: dcline@stat.tamu.edu
Office Hours: TBA or by appointment.  (My Schedule)
Course Web Page: http://stat.tamu.edu/~dcline/615.html
Text:
References: (to be placed on reserve in Evans Library) F. Beichelt, Stochastic Processes in Science, Engineering and Finance.
M.A. Berger, An Introduction to Probability and Stochastic Processes.
R.N. Bhattacharya and E.C. Waymire, Stochastic Processes with Applications.
E. Cinlar, Introduction to Stochastic Processes.
E.P.C. Kao, An Introduction to Stochastic Processes.
S. Karlin and H.M. Taylor, A First Course in Stochastic Processes.
M. Kijima, Markov Processes for Stochastic Modeling.
S.M. Ross, Stochastic Processes, 2nd ed.
Prerequisite: Statistics 610 or equivalent (that is, a good course on probability distribution theory, including conditional distributions, conditional expectations, moment generating functions, law of large numbers and central limit theorem).  The mathematics requirement is advanced calculus, specifically knowing how to do good proofs and understanding limits, integrals and series, and Laplace transforms.  Measure theory is not required.
I will not, however, be reviewing 610 material.
Grading: Homework – 35%.  Please see the homework policy below.
Midterm Exam – 25%.  Please see the exam policy below.
Final Exam – 40%. 
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 Outline

Topic (by chapter in the text)
1. Introduction  
2. Countable State Markov Chains  
3. Renewal Processes  
4. Point Processes  
5. Countable State Markov Processes  
6. Brownian Motion  

Lecture Notes (PDF) Login required.

Lecture Notes: The lecture notes will be scanned and posted here, as they are ready.
Corrections and Changes: as of 11/07/08.

Homework Assignments (PDF) Login required.

Assignments: Assignments will be posted regularly here.  Please see the homework policy below.

Exam Information

Exams: Information about the exams will be posted here.  Please see the exam policy below.
  • Midterm Exam: Monday, 20 October, 3:00-5:00pm, in Blocker 411.  This exam will cover chapters 1 and 2 of the notes, and the first part of Chapter 3: generating functions, random walks, simple (discrete time) branching processes, stopping times, countable state Markov chains, Lebesgue-Stieltjes integration, Laplace transforms, basic renewal processes, and so on.
    You may bring your lecture notes, including notes you took in class.  No other resources are allowed, including the textbook, homework and solutions.  You may, however, quote (by memory) results proven in the homework.
    Here are two recent midterm exams: Exam 1 (2003) and Exam 1 (2005).  These old exams are meant to give you an idea of the style of questions I will ask, not necessarily the topics of those questions.  (Note that they only covered chapters 1 and 2.)

    (10/24/08) Here are solutions to the midterm exam.

  • Final Exam: Tuesday 9 December, 10:00am–12:30pm, in Blocker 411.  Note the early start.
    You may bring your lecture notes and the textbook.  No other resources are allowed, including homework and solutions.  You may, however, quote (by memory) results proven in the homework.

Course Policies

Homework Policy: Your homework solutions must be your own work, not from outside sources, consistent with the university rules on academic dishonesty.  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) and copies of pages from solutions manuals.
  • 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, consistent with the university rules on academic dishonesty.  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.
  • Incomplete grades will be given only in the event that circumstances beyond your control cause prolonged absence from class and the work cannot be made up.

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 to first get written permission from me (Daren B.H. Cline, TAMU Department of Statistics, College Station TX 77845-3143).