Other references for Stat 330/600
- Ash, R. B. Real Analysis and Probability
Good background on measure theory, particularly the connections
between topology and measure.
Recommended for martingales and conditioning.
- Billingsley, P. Probability and Measure
Very well written. Particularly recommended for the discussion on
conditioning. Covers many
topics that might have been included in this course.
- Breiman, L. Probability
A good book to look at after you think you know what is going
on. Deceptive at times, because
hard ideas are made to seem easy. Very good for weak convergence,
and more advanced topics. Worth owning.
- Chow, Y. S. and Teicher, H. Probability theory:
Written in a technical style, but full of information. Good on
martingales and exchangeability.
When I first looked at this book I didn't like it, but now I refer to
- Chung, K. L. A Course in Probability Theory
A standard text. Too dry for my taste. A good place to look for
- Dudley, R. M. Real Analysis and Probability
A thorough text that has become one of my favourites. Read the notes
at the end of
each chapter to see how a real scholar works. Highly recommended.
- Feller, W. An Introduction to Probability Theory and Its
A classic. If you are serious about probability theory you need to own
this book (and the
companion volume~I). Covers lots of material not found in other
texts. Very good on
characteristic functions; very little on martingales. Unfortunately,
Feller tried to avoid
- Folland, G. B. Real Analysis:Modern Techniques and Their
Excellent source for measure theory and real analysis.
- Kolmogorov, A. N. Foundations of the Theory of
The original. It contains most of what goes into a modern probability
course, in under a hundred pages.
Hard reading, because notation and fashion have changed, but the ideas
are mostly all there.
Martingale theory wasn't invented in~1933, when the book first
appeared. A landmark in the
history of probability.
- Loève, M. Probability Theory
The classic text on probability. I refer to it occasionally. The
latest edition comes in two
- Pollard, D. Convergence of Stochastic Processes
I will borrow (with modifications) some material from Chapter~III for
weak convergence and the
central limit theorem.
- Royden, H. L. Real Analysis
An excellent reference for measure theory. Read Chapters~11 and~12 in
- Whittle, P. Probability via Expectation
Expectations as the starting point for the development of probability
theory; similar to my
approach. Very clear.
- Williams, D. Probability with Martingales
A tad eccentric, but superbly clear. An author who conveys his
enthusiasm for a great
subject. Worth at least a browse at some stage during the course.