1. Finitely additive functions in measure theory and applications
- Author
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Daniel Alpay and Palle Jorgensen
- Subjects
hilbert space ,reproducing kernels ,probability space ,gaussian fields ,transforms ,covariance ,itô integration ,itô calculus ,generalized brownian motion ,Applied mathematics. Quantitative methods ,T57-57.97 - Abstract
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.
- Published
- 2024
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