Document Type
Article
Publication Date
1-20-2016
Abstract
For a general class of Gaussian processes W, indexed by a sigma-algebra F of a
general measure space (M,F, _), we give necessary and sufficient conditions for the validity
of a quadratic variation representation for such Gaussian processes, thus recovering _(A),
for A 2 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.
Recommended Citation
Alpay, D., Jorgensen, P., Levanony, D., 2016. On the Equivalence of Probability Spaces. Journal of Theoretical Probability. doi:10.1007/s10959-016-0667-7
Peer Reviewed
1
Copyright
Springer
Comments
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Theoretical Probability in 2016 following peer review. The final publication is available at Springer via http://dx.doi.org/10.1007/s10959-016-0667-7