Statisitcs 218: Stochastic Processes
Professor Joseph Romano, romano@stat.stanford.edu
MWF 1:15 - 2:05, Applied Physics 200
Office Hours: 142 Sequoia Hall, Monday 2:15-3:15
and Friday 11:00-12:00
Teaching Assistants:
The teachings assistants are Ery Arias-Castro and Jie Peng.
Jie's office hours will be Wednesday from 10-12, Room 237
in Sequoia Hall.
Ery's office hours will be 10-11 Tuesdays and Thursdays, Room 141 in Sequoia Hall.
Texts and background material
The required textbook is Taylor and Karlin's
An Introduction to Stochastic Modeling, 3rd edition,
published by Academic Press. Optional texts
are Stochastic Processes by Ross, published by Wiley,
and A First Course in Stochastic Processes, by Karlin
and Taylor, published by Academic Press.
Syllabus
This is a rough outline of some of the topics:
- Some Basic Markov Chains, Branching Processes, Random Walks,
Generating Functions
- Poisson Processes, Renewal Theory, Renewal Theorems,
Regenerative Processes and applications
- Some Continuous Time Markov Chains, Birth and Death
Processes, Queueing Systems
- Gaussian Processes and Brownian Motion
- Martingales, Basic Convergence Theorems, and applications
- Stationary Processes, Time Series, Prediction
Problem sets
- Problem Set 1: (Due Friday April 12) From Chapter III of the
text: Exercises 8.2, 8.3, Problems 8.2, 8.3, Problems 9.1, 9.5, 9.9.
Solutions are HERE
- Problem Set 2: (Due Friday April 19) Click
HERE. For solutions click
Here
- Problem Set 3: (Due Friday April 26) Click
HERE For solutions click
Here
- Problem Set 4: (Due Friday May 10) From Chapter VIII of the
text: Problem 1.5 on page 489. Problems 2.1-2.6 on pages 497-498.
Note there is a typo in Problem 2.4. The very last symbol m
should be z. Solutions are HERE
- Problem Set 5: (Due Friday May 17) From Chapter VIII of the
text: Problems 3.1, 3.5, 3.6, 3.7, 3.9, 4.1, 4.3.
For solutions click HERE
- Problem Set 6: (tentatively Due Friday May 24) From Chapter VIII
of the text: Problems 4.6, 4.7, 4.8. From Chapter IX of
the text: Problems 2.1, 2.2, 3.1, 3.2. (You may substitute
2.6 for 3.2.)
For solutions click HERE
Handouts