- Tytuł:
- Finitely additive functions in measure theory and applications
- Autorzy:
-
Alpay, Daniel
Jorgensen, Palle - Powiązania:
- https://bibliotekanauki.pl/articles/29519748.pdf
- Data publikacji:
- 2024
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Hilbert space
reproducing kernel
probability space
Gaussian field
transforms
covariance
Itô integration
Itô calculus
generalized Brownian motion - Opis:
- 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 μ-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 μ, and to adjoints of composition operators.
- Źródło:
-
Opuscula Mathematica; 2024, 44, 3; 323-339
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł