Bibliographic Details
| Title: |
Finitely additive functions in measure theory and applications |
| Authors: |
Daniel Alpay, Palle Jorgensen |
| Source: |
Opuscula Mathematica, Vol 44, Iss 3, Pp 323-339 (2024) |
| Publisher Information: |
AGH Univeristy of Science and Technology Press, 2024. |
| Publication Year: |
2024 |
| Collection: |
LCC:Applied mathematics. Quantitative methods |
| Subject Terms: |
hilbert space, reproducing kernels, probability space, gaussian fields, transforms, covariance, itô integration, itô calculus, generalized brownian motion, Applied mathematics. Quantitative methods, T57-57.97 |
| More Details: |
In this paper, we consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of \(\mu\)-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures \(\mu\), and to adjoints of composition operators. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
1232-9274 |
| Relation: |
https://www.opuscula.agh.edu.pl/vol44/3/art/opuscula_math_4416.pdf; https://doaj.org/toc/1232-9274 |
| DOI: |
10.7494/OpMath.2024.44.3.323 |
| Access URL: |
https://doaj.org/article/6571d1d93aaf467780858bebd8c3ddcd |
| Accession Number: |
edsdoj.6571d1d93aaf467780858bebd8c3ddcd |
| Database: |
Directory of Open Access Journals |
