La décomposition spectrale d’un élément aléatoire banachique :cas Séries périodiquement corrélées

Abstract

The objective of this chapter is to present an algorithm of decomposition of a banachic random element of integrable square norm (random variable, operator of covariance) of the Kharhunen-Loève type. Indeed, from the spectral decomposition of a positive symmetric compact operator of L (E '; E), where E is a separable real Banach space and E ' its topological dual, the canonical development is given for a random elements from second-order to values in Banach space E. As a special case we improve certain well-known results (see A.Wiener (1976), V.I.Tarieladze(1980) , N.N.Vakhania(1993), C.R.Baker and IW.McKeague(1981)) and on the other hand we give an explicit form of a random elements with values in the Banach space E, of its covariance operator and its nuclear standard. The results of this chapter are published in the International Journal of Statistics and Economics.