Locally stationary harmonizable complex improper stochastic processes


Patrik Wahlberg, Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino (TO), Italy.


This article concerns continuous-time second-order complex-valued improper stochastic processes that are harmonizable and locally stationary in Silverman's sense. We study necessary and sufficient conditions for the property of local stationarity in the time and frequency domains. A sufficient condition by Silverman is generalized and extended to the improper case. We obtain a result on the absolute continuity of the complementary spectral measure with respect to the spectral measure, which is related to a spectral characterization of improper wide-sense stationary processes.