Positivity

, Volume 15, Issue 1, pp 105–134 | Cite as

Locally stationary stochastic processes and Weyl symbols of positive operators

Article

Abstract

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.

Keywords

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

Mathematics Subject Classification (2000)

60G20 60G10 42A82 47G30 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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