Change of Measures for Spectral Stochastic Integrals

2020/06/10 by Yu-Lin Chou, Chou, Yu-Lin
Computer Science · #37M10 #60A10 #60G10 #60H05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2006.05834

openalex publication_date 2020/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-Nikodým 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 L² 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.

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