MATH / STAT 492 (498): Introduction to Stochastic Processes

Winter Quarter 2014: Syllabus (last updated 12/9/2013)

Course personnel:

• Professor: Jon A. Wellner
• B320 Padelford Hall
• Phone: 543-6207
• Office hours: 1:30 - 3:30 MWF; or by appointment
•  
• Teaching Assistant: Shuliu Yuan
• B224 Padelford Hall
• Office hours: 10:30-12:30, Tuesday and Thursday

Administrative Information:

• Time(s): TTh 10:30 - 12:00
  
• Place: CSSS Conference Room, Padelford C14A

Prerequisites:

• Probability Math/Stat 395 and successful completion of Math/Stat 491
• An interest in stochastic processes

Required Texts:

• Essentials of Stochastic Processes, 2nd Edition, by Richard Durrett.
• A First Course in Stochastic Processes, 2nd Edition, by S. Karlin and H. Taylor

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. (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.

Grading:

• Homework: 20%
• Midterm: 20%: Thursday, February 13 (in class).
• Project: 20% (due Friday 14 March).
• Final: 40%
  (Scheduled time & date: Monday, March 17, 10:30-12:20)

Lectures:

• Chapter 1. Renewal theory (Ross chapter 3; Karlin & Taylor chapter 5)
• Chapter 2. Martingales revisited; Karlin and Taylor, chapter 6
• Chapter 3. Brownian motion; introduction, chapter 7
• Chapter 4. Brownian motion; connections with analysis: Kac's formula
• Chapter 5. Stationary processes; Karlin and Taylor chapter 9

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