On the hellinger square integral with respect to an operator valued measure and stationary processes |
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Authors: | Andrzej Makagon |
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Institution: | Institute of Mathematics, Wroclaw Technical University, 50-370 Wroclaw, Poland |
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Abstract: | A construction of the Hellinger square integral with respect to a semispectral measure in a Banach space B is given. It is proved that the space of values of a B-valued stationary stochastic process is unitarily isomorphic to the space of all B1-valued measures that are Hellinger square integrable with respect to the spectral measure of the process. Some applications of the above theorem in the prediction theory (especially to interpolation problem) are also considered. |
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Keywords: | 60G25 47D05 28B05 Hellinger square integral semispectral measure dilation of a semispectral measure stationary process linear prediction |
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