Commutative monads as a theory of distributions

Anders Kock

Commutative monads as a theory of distributions

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

28 Citations (Scopus)

Abstract

It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered here are the notions of convolution, density, expectation, and conditional probability.

Original language	English
Journal	Theory and Applications of Categories
Volume	26
Issue	4
Pages (from-to)	97-131
Number of pages	35
ISSN	1201-561X
Publication status	Published - 2012

Keywords

monads
distributions
extensive quantities

Access to Document

http://www.tac.mta.ca/tac/volumes/26/4/26-04.pdf

Cite this

@article{aee3f03a700b441e8596f240ca5c906b,

title = "Commutative monads as a theory of distributions",

abstract = "It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered here are the notions of convolution, density, expectation, and conditional probability.",

keywords = "monads, distributions, extensive quantities",

author = "Anders Kock",

year = "2012",

language = "English",

volume = "26",

pages = "97--131",

journal = "Theory and Applications of Categories",

issn = "1201-561X",

publisher = "Mount Allison University",

number = "4",

}

TY - JOUR

T1 - Commutative monads as a theory of distributions

AU - Kock, Anders

PY - 2012

Y1 - 2012

N2 - It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered here are the notions of convolution, density, expectation, and conditional probability.

AB - It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered here are the notions of convolution, density, expectation, and conditional probability.

KW - monads

KW - distributions

KW - extensive quantities

M3 - Journal article

SN - 1201-561X

VL - 26

SP - 97

EP - 131

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

IS - 4

ER -

Commutative monads as a theory of distributions

Abstract

Keywords

Access to Document

Fingerprint

Cite this