|
This article is cited in 1 scientific paper (total in 1 paper)
Categorial Independence and Lévy Processes
Malte Gerholdab, Stephanie Lachsa, Michael Schürmanna a Institute of Mathematics and Computer Science, University of Greifswald, Germany
b Department of Mathematical Sciences, NTNU Trondheim, Norway
Abstract:
We generalize Franz' independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms. We will see that this only works consistently if the unit object is an initial object, in which case the inclusions can be defined starting from the tensor category alone. The obtained independence for morphisms is called categorial independence. We define categorial Lévy processes on every tensor category with initial unit object and present a construction generalizing the reconstruction of a Lévy process from its convolution semigroup via the Daniell–Kolmogorov theorem. Finally, we discuss examples showing that many known independences from algebra as well as from (noncommutative) probability are special cases of categorial independence.
Keywords:
general independence, monoidal categories, synthetic probability, noncommutative probability, quantum stochastic processes.
Received: March 28, 2022; in final form September 30, 2022; Published online October 10, 2022
Citation:
Malte Gerhold, Stephanie Lachs, Michael Schürmann, “Categorial Independence and Lévy Processes”, SIGMA, 18 (2022), 075, 27 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1871 https://www.mathnet.ru/eng/sigma/v18/p75
|
Statistics & downloads: |
Abstract page: | 39 | Full-text PDF : | 28 | References: | 8 |
|