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Get Access to Full TextLet be a Banach space of all ℙ-square integrable random variables defined on some probability space with values in the complex separable Banach space E. For an -valued stationary continuous random function on the locally compact abelian group G, we provide a condition of existence of a random measure Z taking values in such that has a spectral representation as a Fourier transform of Z.
Keywords: Random measures; stationary random function; Fourier transform; stochastic integrals; spectral measures
Received: 2012-08-05
Revised: 2013-09-23
Accepted: 2014-02-28
Published Online: 2014-05-17
Published in Print: 2014-06-01
Funding Source: Agence Nationale de Recherche Universitaire (A.N.D.R.U.) in P.N.R.
Award identifier / Grant number: No. 46/1
Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2014-0023.
© 2014 by Walter de Gruyter Berlin/Boston.
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