Finitely additive functions in measure theory and applications

• Autorzy: Alpay Daniel , Jorgensen Palle

Identyfikatory

DOI

10.7494/OpMath.2024.44.3.323

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hilbert space; reproducing kernel; probability space; Gaussian field; transforms; covariance; Itô integration; Itô calculus; generalized Brownian motion

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 3
• Strony: 323--339
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Alpay Daniel

• Schmid College of Science and Technology, Chapman University, One University Drive Orange, California 92866, USA

• https://orcid.org/0000-0002-7612-3598

autor

Jorgensen Palle

• The University of Iowa, Department of Mathematics, 14C McLean Hall, Iowa City, IA 52246, USA

• https://orcid.org/0000-0003-2681-5753

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)