2025/04/04 by Patrik Wahlberg, Wahlberg, Patrik
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Random Matrices and Applications #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2504.03493
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.