Journal article
Operator theory of multiple Ito-integrals
Journal of operator theory, Vol.93(2), pp.477-509
06/15/2025
DOI: 10.7900/jot.2023jun14.2428
Abstract
We study systems of Gaussian fields indexed by families F of positive sigma-finite measures μ. For a given μ, the corresponding Gaussian field W(μ) is centered and has quadratic variation equal to μ. Our focus is the induced multi-variable case of stochastic analysis and discrete time Gaussian random walk processes. The approach is operator-theoretic with three aims: (i) explicit formulas for the operators and Hilbert spaces involved; (ii) implications for Krein-Feller diffusion processes; and (iii) a study of operator systems and algebras generated by the W(μ)-induced Ito-isometries Vμ, for μ in F.
Details
- Title: Subtitle
- Operator theory of multiple Ito-integrals
- Creators
- Palle E.T. JorgensenJames Tian
- Resource Type
- Journal article
- Publication Details
- Journal of operator theory, Vol.93(2), pp.477-509
- Publisher
- THETA FOUNDATION
- DOI
- 10.7900/jot.2023jun14.2428
- ISSN
- 0379-4024
- eISSN
- 1841-7744
- Language
- English
- Date published
- 06/15/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984824332302771
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