A. Boudou and S. Viguier-Pla (2019)
Proximité entre mesures aléatoires et entre séries
stationnaires associées.
Séminaire de Statistique, Institut de Mathématiques de Toulouse,
Toulouse.
- Classification
- 60G57, 60G10, 60B15, 60H05
- Keywords
- Random measure, Stationnary series,
spectral measure, convolution product, projector, relation of order
Abstract :
Any stationary series is a Fourier transform of a random measure. So we can
guess that when two stationary series are close together, so it is for their
associated random measures, and conversely, the proximity between two random
measures induces the proximity between the associated stationary series.
It is this kind of question that we propose considering in this seminar.
The choice of the distance is determinant for this correspondence. We give a
definition of a distance between stationary series, of a distance
between random measures, and then develop some mathematical tools.
.