Properties of Hida processes on 2. 2. Prediction and interpolation problems for processes on 2 |
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Authors: | Bernard Prum |
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Institution: | Statistique Appliquée Mathematique, Paris, France |
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Abstract: | The properties of N-Hida processes Part 1 (B. Prum, 1984, J. Multivar. Anal.15, 336–360) are studied when the indices set is 2. First, the past of a point (s, t) of 2 is extended to st = σ{γuv, u ≤ s or v ≤ t}. The dimension of the linear space generated by the conditional expectations of an N-Hida process γz when z goes over a p × q lattice is bounded by N(p + q ? 1). The same problem is then considered when the expectations are taken conditionally to the field generated by the process outside of a rectangle, and the bound of the dimension of the linear space generated on a lattice is also given. Special attention is devoted to the case when γz is a combination of strong martingales. |
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Keywords: | 60G60 60J25 82A67 multiparameter processes Markov property prediction interpolation |
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