Relation between unit operators proximity and their associated spectral measures

Alain Boudou , Sylvie Viguier-Pla

In this paper, we study how the locally concentration of the spectral measure expresses 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.

Mots clés: 60G57; 60G10; 60B15; 60H05; Random measures; Stationnary processes; Fourier transform; Stochastic integrals; Spectral measures

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Alain Boudou, Sylvie Viguier-Pla. Relation between unit operators proximity and their associated spectral measures. Statistics and Probability Letters, 2010, ⟨10.1016/j.spl.2010.07.016⟩. ⟨hal-00691783⟩