Locally stationary stochastic processes and Weyl symbols of positive operators

The paper treats locally stationary stochastic processes. A connection with the Weyl symbols of positive operators is observed and explored. We derive necessary conditions on the two functions that constitute the covariance function of a locally stationary stochastic process, some of which use this connection to time-frequency analysis and pseudodifferential operators. Finally, we discuss briefly the subclass of Cohen’s class of time–frequency representations having separable kernels, which is related to locally stationary stochastic processes.