# Probability

July 29, 2011 — July 15, 2019

algebra

functional analysis

probability

A placeholder where I mention some things I occasionally refer people to or have been referred to, but forget the reference for.

Terry Tao, and his Neat Probability Hacks for Dummies

Dominic Yeo

## 1 Rényi axioms

Founded on conditional probability (Mečíř 2020; Taraldsen 2019).

## 2 Cox probability

Also founded on conditional probability, but more Bayesey I think. See Cox probability

## 3 References

Aldous. 1981. “Representations for Partially Exchangeable Arrays of Random Variables.”

*Journal of Multivariate Analysis*.
———. 1985. “Exchangeability and Related Topics.” In

*École d’Été de Probabilités de Saint-Flour XIII — 1983*. Lecture Notes in Mathematics.
Applebaum. 2009.

*Lévy Processes and Stochastic Calculus*. Cambridge Studies in Advanced Mathematics 116.
Bao, and Ullah. 2009. “Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications.” 200907. Working Papers.

Baudoin. 2014.

*Diffusion Processes and Stochastic Calculus*. EMS Textbooks in Mathematics.
Burgess. 2014. “Martingale Measures & Change of Measure Explained.” SSRN Scholarly Paper ID 2961006.

Campbell, Syed, Yang, et al. 2019. “Local Exchangeability.”

*arXiv:1906.09507 [Math, Stat]*.
Cosma Rohilla Shalizi. 2007.

*Almost none of the theory of stochastic processes*.
Diaconis, and Freedman. 1980. “De Finetti’s Theorem for Markov Chains.”

*The Annals of Probability*.
Fleming, and Harrington. 2005. “Appendix A: Some Results from Stieltjes Integration and Probability Theory.” In

*Counting Processes and Survival Analysis*.
Gray. 1987.

*Probability, Random Processes, and Ergodic Properties*.
Grinstead, and Snell. 1997.

*Introduction to Probability*.
Hanson, and Wright. 1971. “A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables.”

*Annals of Mathematical Statistics*.
Jacod, and Shiryaev. 1987.

*Limit Theorems for Stochastic Processes*. Grundlehren Der Mathematischen Wissenschaften.
Kallenberg. 2017.

*Random Measures, Theory and Applications*.
Mathai, and Provost. 1992.

*Quadratic Forms in Random Variables: Theory and Applications*. Statistics, Textbooks and Monographs, v. 126.
Mečíř. 2020. “Foundations for Conditional Probability.”

Nau. 2001. “De Finetti Was Right: Probability Does Not Exist.”

*Theory and Decision*.
Peng. 2007. “G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type.” In

*Stochastic Analysis and Applications*.
Pitman, and Yor. n.d. “A Guide to Brownian Motion and Related Stochastic Processes.”

Rényi. 1970.

*Foundations of Probability*.
Resnick. 1992.

*Adventures in Stochastic Processes*.
Soch, Proofs, Faulkenberry, et al. 2020. “StatProofBook/StatProofBook.github.io: StatProofBook 2020.”

Taraldsen. 2019. “Conditional Probability in Rényi Spaces.”

Ullah, and Bao. 2007. “Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications.”

van Zanten. 2004.

*An introduction to stochastic processes in continuous time*.
Wright. 1973. “A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables Whose Distributions Are Not Necessarily Symmetric.”

*Annals of Probability*.