MATH / STAT 491: Introduction to Stochastic Processes

Fall Quarter 2014: Syllabus (last updated 09/16/2014)

Course personnel:

• Professor: Hari Narayanan
• B301 Padelford Hall
• Phone: 206 543-5169
• Office hours: 1:30 - 2:30 MWF; or by appointment
• Teaching Assistant: Shuliu Yuan
• Stat study center CMU B023
• Office hours: 10:30 - 12:30 Tue-Thu; or by appointment

Administrative Information:

• Time(s): MWF 11:30 - 12:20
  
• Place: ANDERSON 008

Prerequisites:

• Probability Math/Stat 395

Required Texts:

• Essentials of Stochastic Processes, 2nd Edition, by Richard Durrett.
• Introduction to Probability Models , 10th Edition, by Sheldon Ross.

Supplemental texts:

• Breiman, L. (1969). Probability and stochastic processes with a view toward applications. Houghton Mifflin, Boston.
• Cinlar, E. (1975). Introduction to stochastic processes. Prentice-Hall, Englewood Cliffs, N.J.
• Hoel, P.G., Port, S.C., and Stone, C.J. (1972). Introduction to stochastic processes. Houghton Mifflin, Boston.
• Karlin, S. and Taylor, H. M. (1975). A first course in stochastic processes. Academic Press, New York.
• Karlin, S. and Taylor, H. M. (1981). A second course in stochastic processes Academic Press, New York.
• Lawler, G. F. (2006). Introduction to stochastic processes. Chapman and Hall, Boca Raton, Florida.
• Resnick, S. (1992). Adventures in stochastic processes. Birkhauser, Boston.
• Ross, S. M. (1996). Stochastic processes. Wiley, New York.
• Wasserman, L. (2004). All of Statistics. Springer texts in Statistics

Notes:

• Notes I
• Markov Chain Outline
• Markov Chain Proofs
• Markov Chain Proofs II
• Martingales
• Martingales Updated
• Poisson Processes
• Random Sums

Grading:

• Homework: 20%
• Midterm I: 20%: Monday, October 27 (in class).
• Midterm II: 20%: Friday, November 21 (in class).
• Final: 40%
  (Scheduled time & date: 2:30 - 4:20, Wednesday, December 10).

Assignments:

• Assignment 1 is due on Monday, 6 October.
  
• Solutions 1
• Assignment 2 is due on Monday, 20 October.
  
• Solutions 2
• Assignment 3 is due on Wednesday, 5 November.
  
• Solutions 3
• Assignment 4 is due on Monday, 17 November.
  
• Solutions 4
• Assignment 5 is due on Wednesday, 3 December.
  
• Solutions 5
• Assignment 6
• Solutions 6

Midterm Solutions:

• Midterm I
  
• Midterm II
  

Lectures:

• Chapter 1. Probability review and conditional expectations
• Chapter 2. Markov chains, part I: classification of states
• Chapter 3. Markov chains, part II: limiting behavior and applications.
• Chapter 4. Random walk and martingales
• Chapter 5. Poisson processes

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