论文标题
光谱随机积分的措施的改变
Change of Measures for Spectral Stochastic Integrals
论文作者
论文摘要
在轻度条件下，可以从几乎纯粹的量度理论因素中获得，并且在没有任何特定引用随机过程的情况下，会导致测量变化，类似于通常的radon-nikodým措施的变化，与随机整合的变化相关，以使协方差的光谱代表频谱代表。这些想法自然嵌入了$ l^{2} $空间的希尔伯特空间理论中。预期的主要贡献，包括光谱随机积分措施的完全变化，是光谱随机整合对度量的改变的精致，独立的发展。
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 $L^{2}$ 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.
