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Algebraic probability

If you liked it then you prob’ly put a ring on it

Usefulness: 🔧
Novelty: 💡
Uncertainty: 🤪 🤪 🤪
Incompleteness: 🚧 🚧 🚧

Commonly used algebraic structures over probability, as seen in, for example,

Refs

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

Ressel, Paul. 1991. “Semigroups in Probability Theory.” In Probability Measures on Groups X, edited by Herbert Heyer, 337–63. Springer US. https://doi.org/10.1007/978-1-4899-2364-6_26.

———. 2011. “A Revision of Kimberling’s Results — with an Application to Max-Infinite Divisibility of Some Archimedean Copulas.” Statistics & Probability Letters 81 (2): 207–11. https://doi.org/10.1016/j.spl.2010.11.008.

Ruzsa, Imre, and Gábor J Székely. 1988. Algebraic Probability Theory. John Wiley & Sons Inc.