Probability


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

I wonder if I shoud split off the exchangeability related references? I recently had my interest in that stuff piqued by Said Syed. However, I don’t think it’s likely I’ll be finding time for a deep understanding any time soon.

Aldous, David J. 1985. “Exchangeability and Related Topics.” In École d’Été de Probabilités de Saint-Flour XIII — 1983, edited by David J. Aldous, Illdar A. Ibragimov, Jean Jacod, and P. L. Hennequin, 1–198. Lecture Notes in Mathematics. Springer Berlin Heidelberg.

———. 1981. “Representations for Partially Exchangeable Arrays of Random Variables.” Journal of Multivariate Analysis 11 (4): 581–98. https://doi.org/10.1016/0047-259X(81)90099-3.

Applebaum, David. 2009. Lévy Processes and Stochastic Calculus. 2nd ed. Cambridge Studies in Advanced Mathematics 116. Cambridge ; New York: Cambridge University Press.

Bao, Yong, and Aman Ullah. 2009. “Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications.” 200907. Working Papers. Working Papers. University of California at Riverside, Department of Economics. https://ideas.repec.org/p/ucr/wpaper/200907.html.

Baudoin, Fabrice. 2014. Diffusion Processes and Stochastic Calculus. EMS Textbooks in Mathematics. Zurich, Switzerland: European Mathematical Society.

Burgess, Nicholas. 2014. “Martingale Measures & Change of Measure Explained.” SSRN Scholarly Paper ID 2961006. Rochester, NY: Social Science Research Network. https://papers.ssrn.com/abstract=2961006.

Campbell, Trevor, Saifuddin Syed, Chiao-Yu Yang, Michael I. Jordan, and Tamara Broderick. 2019. “Local Exchangeability.” June 22, 2019. http://arxiv.org/abs/1906.09507.

Cosma Rohilla Shalizi. 2007. Almost None of the Theory of Stochastic Processes.

Diaconis, P., and D. Freedman. 1980. “De Finetti’s Theorem for Markov Chains.” The Annals of Probability 8 (1): 115–30. https://doi.org/10.1214/aop/1176994828.

Fleming, Thomas R, and David P Harrington. 2005. “Appendix A: Some Results from Stieltjes Integration and Probability Theory.” In Counting Processes and Survival Analysis, 317–29. John Wiley & Sons, Ltd. https://doi.org/10.1002/9781118150672.app1.

Gray, Robert M. 1987. Probability, Random Processes, and Ergodic Properties. Springer.

Grinstead, Charles M, and J Laurie Snell. 1997. Introduction to Probability. American Mathematical Society.

Hanson, D. L., and F. T. Wright. 1971. “A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables.” Annals of Mathematical Statistics 42 (3): 1079–83. https://doi.org/10.1214/aoms/1177693335.

Jacod, Jean, and Albert N. Shiryaev. 1987. Limit Theorems for Stochastic Processes. Vol. 288. Grundlehren Der Mathematischen Wissenschaften. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-02514-7.

Kallenberg, Olav. 2017. Random Measures, Theory and Applications. Springer.

Mathai, A. M., and Serge B. Provost. 1992. Quadratic Forms in Random Variables: Theory and Applications. Statistics, Textbooks and Monographs, v. 126. New York: M. Dekker.

Peng, Shige. 2007. “G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type.” In Stochastic Analysis and Applications, edited by Fred Espen Benth, Giulia Di Nunno, Tom Lindstrøm, Bernt Øksendal, and Tusheng Zhang, 541–67. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-70847-6_25.

Pitman, Jim, and Marc Yor. n.d. “A Guide to Brownian Motion and Related Stochastic Processes,” 101. https://www.stat.berkeley.edu/~aldous/205B/pitman_yor_guide_bm.pdf.

Resnick, Sidney I. 1992. Adventures in Stochastic Processes. Birkhauser.

Ullah, Aman, and Yong Bao. 2007. “Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications,” August, 16.

Wright, F. T. 1973. “A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables Whose Distributions Are Not Necessarily Symmetric.” Annals of Probability 1 (6): 1068–70. https://doi.org/10.1214/aop/1176996815.

Zanten, Harry van. n.d. An Introduction to Stochastic Processes in Continuous Time.