Probability Library

Dr Harry Crane asked for recommendations for a “Probability Library”.

These are some of the recommendations:

Harry Crane:

1. Technical: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition
2. Classic: Foundations of the Theory of Probability: Second English Edition (Dover Books on Mathematics) by Kolmogorov
3. Real World: Antifragile. NNTaleb recommended Statistical Consequences of Fat Tails (book in the works) instead over Antifragile.
4. Application: Beyond Counting : Exploiting Casino Games from Blackjack to Video Poker by James Grosjean.
5. Biography: A man for all ages by Ed Thorpe.

Nassim Taleb:

1. Probability Theory I, 4th Edition and Vol 2 by Loeve
2. Methods of Mathematical Finance by Karatzas and Shreve
3. Elements of Information Theory 2nd Edition by Cover and Thomas
4. Probability and measure, 3rd edition by Patrick Billingsley
5. Chance and Stability, Stable Distributions and Their Applications by Uchaikin, Vladimir V. / Zolotarev, Vladimir M. PDF
6. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance by Gennady Samorodnitsky, M.S. Taqqu
7. Stochastic Processes by J. L. Doob
8. Limit distributions for sums of independent random variables by B.V.Gnedenko and A.N.Kolmogorov.
9. Extreme Value Theory by Laurens de Haan and Ana Ferreira
10. Extreme Value Theory (PDF) by Embrechts et. al.

Misc:

via https://twitter.com/BristOliver

• Feller vol 1

• Kolmogorov/Gnedenko

• Petrov Sums of Independent RVs

• Grimmett Percolation

• David Williams Martingales

• Kallenberg’s Foundations of Modern Probability

• Ten Great Ideas about Chance by Persi Diaconis and Brian Skyrms

• Linear Algebra with Probability Oliver Knill for Harvard College Course Math 19b