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

the convolution semigroup, used in divisible processes (what do you call the semigroup of maximum processes?)

in the general transition semigroup of Markov processes.
Refs
 Ress11: (2011) A revision of Kimberling’s results — With an application to maxinfinite divisibility of some Archimedean copulas. Statistics & Probability Letters, 81(2), 207–211. DOI
 RuSz88: (1988) Algebraic probability theory. John Wiley & Sons Inc
 Appl09: (2009) Lévy processes and stochastic calculus. Cambridge ; New York: Cambridge University Press
 Ress91: (1991) Semigroups in Probability Theory. In Probability Measures on Groups X (pp. 337–363). Springer US DOI