Locally stationary stochastic processes and Weyl symbols of positive operators

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Locally stationary stochastic processes and Weyl symbols of positive operators

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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2010 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Econometrics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Potential Theory
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0044-1
Publisher site
See Article on Publisher Site

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.

Journal

PositivitySpringer Journals

Published: Jan 28, 2010

References

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