Summary
We give a decomposition of the two-parameter real Wiener process (W(x, y), (x, y)∈(ℝ+)2 by using the Fourier transform defined on the group which leave it invariant. Then we use this decomposition to obtain some prediction results for this process, which allow us to give upper and lower bounds for the correlation coefficient of the vector-spaces respectively generated by the two families {W(x, y), xy ε≦s} and {W(x, y), xy ε≧t}, 0s t, ε∈{-1,1}.
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Carraro, L. Problèmes de prediction pour le processus de Wiener a deux parametres. Probab. Th. Rel. Fields 72, 619–635 (1986). https://doi.org/10.1007/BF00344724
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DOI: https://doi.org/10.1007/BF00344724