TY  - JOUR
ID  - Alpay2024
LB  - Alpay2024
AU  - Alpay, Daniel
AU  - Jorgensen, Palle
TI  - Finitely additive functions in measure theory and applications
ST  - Finitely additive functions in measure theory and applications
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 3
SP  - 323
EP  - 339
DO  - https://doi.org/10.7494/OpMath.2024.44.3.323
UR  - https://doi.org/10.7494/OpMath.2024.44.3.323
AB  - 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.
KW  - Hilbert space
KW  - reproducing kernels
KW  - probability space
KW  - Gaussian fields
KW  - transforms
KW  - covariance
KW  - Itô integration
KW  - Itô calculus
KW  - generalized Brownian motion
SN  - 1232-9274
ER  -