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首页> 外文期刊>Taiwanese journal of mathematics >White Noise Analysis: Part I. Theory in Progress
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White Noise Analysis: Part I. Theory in Progress

机译：白噪声分析：第一部分，理论进展

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In the past quarter century white noise theory has made great progress. We are further given many interesting and important questions which should be discussed in line with white noise analysis. On the other hand, some of the new directions are before our eyes and they require new analytic methods to be investigated, by generalizing the method established so far. It is now the time to remind the original idea of our stochastic analysis and to think of further directions of this theory which are going to appear in front of us. While we are reviewing the results, we have recognized the foundation of the theory should be refined. This will be done also in Part I. The plan of Part II is as follows. From what have been established, there naturally arise several new topics to be discussed. This is, in a sense, a continuation of Part I. On the other hand, having suggested by many significant examples and problems in applications, we come to a framework of the new white noise theory which is going to be constructed. A significant development is to grow out of L~2-theory and to establish an analysis on a wider class of suitable functionals of sample paths. This approach will be proposed.
机译：在过去的25年中，白噪声理论取得了长足的进步。我们还得到了许多有趣且重要的问题，应该根据白噪声分析来讨论这些问题。另一方面，一些新的方向已经摆在我们的眼前，它们需要通过概括到目前为止建立的方法来研究新的分析方法。现在是时候提醒我们进行随机分析的初衷，并思考将在我们面前出现的该理论的进一步发展方向。在审查结果时，我们已经认识到应该完善该理论的基础。这也将在第一部分中完成。第二部分的计划如下。根据已经建立的内容，自然会产生几个要讨论的新主题。从某种意义上讲，这是第I部分的继续。另一方面，在提出了许多重要的例子和应用中的问题后，我们得出了将要构建的新白噪声理论的框架。一个重要的发展是要从L〜2理论中发展出来，并对更广泛的适用于样本路径的功能类别进行分析。将提出这种方法。

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