The Wigner distribution of Gaussian weakly harmonizable stochastic processes

We define the Wigner distribution of a tempered generalized stochastic process that is complex-valued symmetric Gaussian. This gives a time-frequency generalized stochastic process defined on the phase space. We study its covariance and our main result is a formula for the Weyl symbol of the covariance operator, expressed in terms of the Weyl symbol of the covariance operator of the original generalized stochastic process.

arXiv:2504.03493Applied and Computational Harmonic AnalysisAug 13, 20250 citations

The Wigner distribution of Gaussian weakly harmonizable stochastic processes

BENGT PATRIK MARTIN WAHLBERG

Published Jan 1, 2006• 0 citations

OpenAlex

Related papers

Generalized Stochastic Processes and Wigner Distribution

Wolfgang Hörmann

Jan 1, 19890 citations

The random Wigner distribution of Gaussian stochastic processes with covariance in $S_0 (\R^{2d})$ The random Wigner distribution of Gaussian stochastic processes with covariance in $S_0 (\R^{2d})$

BENGT PATRIK MARTIN WAHLBERG

Jan 1, 20050 citations

Gaussian Wigner distributions: A complete characterization

R. Simon, E. C. G. Sudarshan, Narasimhaiengar Mukunda

Physics Letters ASep 1, 198732 citations

A unified approach to quantum dynamical maps and gaussian Wigner distributions

Francis J. Narcowich, Robert F. O’Connell

Physics Letters ANov 1, 19889 citations

Measurement-induced decoherence and Gaussian smoothing of the Wigner distribution function

Yong-Jin Chun, Hai-Woong Lee

arXiv:quant-ph/0305011Annals of PhysicsJun 2, 20032 citations

The Wigner distribution of Gaussian tempered generalized stochastic processes

Patrik Wahlberg

arXiv:2504.03493Applied and Computational Harmonic AnalysisAug 13, 20250 citations

The random Wigner distribution of Gaussian stochastic processes with covariance in

S_0 (\R^{2d})