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Browsing by Subject "Itô integration"

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    Item type:Article, Access status: Open Access ,
    Finitely additive functions in measure theory and applications
    (Wydawnictwa AGH, 2024) Alpay, Daniel; Jørgensen, Palle E.T.
    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.