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On The Equivalence Of Probability Spaces, Daniel Alpay, Palle Jorgensen, David Levanony
On The Equivalence Of Probability Spaces, Daniel Alpay, Palle Jorgensen, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
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 …