Positivity

, Volume 15, Issue 1, pp 105–134

Locally stationary stochastic processes and Weyl symbols of positive operators

Article

DOI: 10.1007/s11117-010-0044-1

Cite this article as:
Wahlberg, P. Positivity (2011) 15: 105. doi:10.1007/s11117-010-0044-1

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 processesPseudodifferential operatorsOperator positivityTime–frequency analysis

Mathematics Subject Classification (2000)

60G2060G1042A8247G30

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly