Variations of random fields and application to computation

研究期间(2000-2001学年)的计划是研究随机场和相关的计算问题。所取得的主要成果都是基于创新理论，为研究提供了有用的工具。研究结果如下：1.研究结果。高斯随机场：由等高线或闭合曲面参数化的高斯随机场的新息可以通过它的变化来获得。通常，这样的创新是白噪声，它将给定场表示为随机积分。核表示类场依赖方式的概率性质，包括参数排序时的可逆性。一般随机场。对于一个表示为齐次混沌积分的场，我们可以形成新息显式，从而得到最好的预测值。此外，一般加性过程的随机线性函数允许我们以一种非线性的方式形成创新，我们解决了通信理论中的可计算性问题，如跳跃寻找。白噪声理论的应用。在对加性过程的从属关系进行了深入研究的基础上，我们将其应用于黑洞候选X射线数据的处理。在光谱之外，我们计算了它的特征泛函，得到了一个很好的数学模型。

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.