Change of Measures for Spectral Stochastic Integrals
Abstract
Under mild conditions, it is possible to obtain, from almost purely measure-theoretic considerations and without any specific reference to stochastic processes, a change-of-measures result, resembling the usual Radon-Nikod\'ym change of measures, associated with a variant of stochastic integration for a spectral representation of covariance stationary processes; the ideas are naturally embedded in the Hilbert space theory of spaces. The intended main contribution, including a complete proof of change of measures for spectral stochastic integrals, is the refined, self-contained developments of spectral stochastic integration toward change of measures.
Keywords
Cite
@article{arxiv.2006.05834,
title = {Change of Measures for Spectral Stochastic Integrals},
author = {Yu-Lin Chou},
journal= {arXiv preprint arXiv:2006.05834},
year = {2020}
}
Comments
Two slight but not insubstantial improvements to increase clarity, adding back the missing word "disjoint" to the definition of an orthogonal elementary stochastic measure, and deleting some out-of-context words regarding $\mathscr{A}$-simple functions