On multivariate fractional random fields: Tempering and operator-stable laws

In this paper, we define a new and broad family of vector-valued random fields called tempered operator fractional operator-stable (TRF, for short). TRF is typically non-Gaussian generalizes stable stochastic processes. comprises moving average harmonizable-type subclasses that are constructed by tempering (matrix-) homogeneous, matrix-valued kernels in time- Fourier-domain integrals with respect to vector-valued, strictly measures. We establish the existence fundamental properties TRF. Assuming both Gaussianity isotropy, show equivalence between certain harmonizable addition, sample path scalar-valued case several Gaussian instances.