Variations of random fields and application to computation

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The plan during the research period (2000 - 2001 academic year) is to study random fields and related problems of computation. The main results have been obtained are all based on the Innovation Theory, which provides useful tools of study. The results are as follows.1. Gaussian random fields.The innovation of a Gaussian random field parameterized by a contour or a closed surface can be obtained by its variation. Usually, such an innovation is a white noise, by which the given field is expressed as a stochastic integral. The kernel represents the probabilistic properties of the field like way of dependence including reversibility when the parameters are ordered.2. General random fields.For a field expressed as an integral of homogeneous chaos we can form innovations explicity, so that the best predictor is obtained. Also, random linear functions of a general additive process allow us to form innovation in a nonlinear manner, and we solved the computability problems, like jump finding, m the theory of communications.3. Application of white noise theory.Having had profound study on the subordination for additive processes, we applied to the processing of the X-ray data from the black-hole candidate. Beyond the spectrum we have computed its characteristic functional to have a good mathematical model.