Publications

A. Boudou and S. Viguier-Pla (2010)
Relation between unit operators proximity and their associated spectral measures.
Stat. and Prob. Letters 80 , 1724-1732

Classification

60G57, 60G10, 60B15, 60H05

Keywords

Random measures, Stationary processes, Fourier transform, Stochastic integrals, Spectral measures

Abstract : In this paper, we study how the local concentration of the spectral measure can be expressed in the temporal domain for stationary processes. For this purpose, we establish an equivalence between the proximity of the shift operators (which are unit operators) and the associated projector-valued spectral measures. An illustration is given.