2022/05/16 by Daniel Alpay, Alpay, Daniel, Palle E. T. Jørgensen +1
Economics, Econometrics and Finance · Mathematics · #47B32 #60G15 #60G20 #60H05 #Advanced Banach Space Theory #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2205.07462
openalex publication_date 2022/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.