, Volume 15, Issue 1, pp 105-134

First online:

Locally stationary stochastic processes and Weyl symbols of positive operators

  • Patrik WahlbergAffiliated withDipartimento di Matematica, Università di Torino Email author 

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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.


Locally stationary generalized stochastic processes Pseudodifferential operators Operator positivity Time–frequency analysis

Mathematics Subject Classification (2000)

60G20 60G10 42A82 47G30