Journal article
On the Equivalence of Probability Spaces
Journal of theoretical probability, Vol.30(3), pp.813-841
09/01/2017
DOI: 10.1007/s10959-016-0667-7
Abstract
For a general class of Gaussian processes W, indexed by a sigma-algebra F of a general measure space (M, F, sigma), we give necessary and sufficient conditions for the validity of a quadratic variation representation for such Gaussian processes, thus recovering sigma(A), for A is an element of F, as a quadratic variation of W over A. We further provide a harmonic analysis representation for this general class of processes. We apply these two results to: (i) a computation of generalized Ito integrals and (ii) a proof of an explicit and measure-theoretic equivalence formula, realizing an equivalence between the two approaches to Gaussian processes, one where the choice of sample space is the traditional path space, and the other where it is Schwartz' space of tempered distributions.
Details
- Title: Subtitle
- On the Equivalence of Probability Spaces
- Creators
- Daniel Alpay - Ben-Gurion University of the NegevPalle Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USADavid Levanony - Ben-Gurion University of the Negev
- Resource Type
- Journal article
- Publication Details
- Journal of theoretical probability, Vol.30(3), pp.813-841
- DOI
- 10.1007/s10959-016-0667-7
- ISSN
- 0894-9840
- eISSN
- 1572-9230
- Publisher
- SPRINGER/PLENUM PUBLISHERS
- Number of pages
- 29
- Grant note
- 2010117 / Binational Science Foundation
- Language
- English
- Date published
- 09/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984240870602771
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