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Canonical Development of second order Banach-valued random element

Benchikh Tawfik, Mankour Khadidja


From the spectral decomposition of the covariance operator of Banach-valued random element, the canonical development is given for second order E-valued random elements. As a particular case we improve some well known results ((Weron, 1976), (Tarieladze, 1980),(Vakhania, 1993), (Baker and McKeague, 1981)). The spectral decomposition yields us to propose an algorithm of orthogonal weak expansion of Banach-valued random elements.


anach space, random element, Covariance operators, Nuclear operators, Gaussian Banach-valued random elements, Spectral decomposition.

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