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
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. 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.
———. 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.
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. http://arxiv.org/abs/1906.09507.
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.
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). Institute of Mathematical Statistics: 1079–83. https://doi.org/10.1214/aoms/1177693335.
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.
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). Institute of Mathematical Statistics: 1068–70. https://doi.org/10.1214/aop/1176996815.