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A study on semi-selfdecomposable distributions and semi-selfsimilar stochastic processes

半自分解分布与半自相似随机过程的研究

基本信息

批准号：
10440033
负责人：
MAEJIMA Makoto
金额：
$ 3.58万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

1. The structure of the classes of semi-selfdecomposable distributions and its nested subclasses were clarified among the class of all infinitely divisible distributions. We introduced a way of making a new class of limitinz distributions derived from a class of distributions by taking the limit through some subsequence of normalized partial sums of independent random variables. We characterized completely a sort of a fixed point of this procedure.2. In contrast to the absolute continuity of all selfdecomposable distributions, we found that semi-selfdecomposable distributions are not necessarily absolutely continuous. We also found a subclass of semi-selfdecomposable distributions which are always absolutely continuous.3. We constructed some examples of non-selfdecomposable (or non-semi-selfdecomposable) distributions whose projections to lower dimensional spaces are selfdecomposable (or semi-selfdecomposable). This property has a sharp contrast to stable distributions.4. We found that the marginal distributions of semi-selfsimilar processes at a time is selfdecomposable. We also found that their joint distributions at several times are closely related to nested subclasses of selfdecomposable distributions. It is also proved that similar observations remain true between selfdecomposable distributions and selfsimilar processes.5. We succeeded in defining multivariate type G distributions and found a necessary and sufficient condition for that they are selfdecomposable. We also defined a sequence of nested subclasses of type G distributions and succeeded in making a new refinement of the class of infinitely divisible distributions.

1.在所有无限可分分布类中阐明了半自可分解分布类及其嵌套子类的结构。本文介绍了一种由一类分布通过独立随机变量的正规化部分和的某个子序列取极限而得到一类新的极限分布的方法。我们完全刻画了这个过程的一种不动点.与所有自分解分布的绝对连续性相反，我们发现半自分解分布不一定是绝对连续的。我们还发现了一个半自分解分布的子类，它总是绝对连续的.我们构造了一些非自分解（或非半自分解）分布的例子，它们到低维空间的投影是自分解（或半自分解）的。这一性质与稳定分布形成鲜明对比。我们发现半自相似过程的边际分布在某个时刻是自分解的。我们还发现，他们的联合分布在几个时间是密切相关的嵌套子类的自分解分布。证明了自分解分布与自相似过程之间的相似性.我们成功地定义了多元G型分布，并找到了它们是自分解的一个充要条件。我们还定义了一系列的嵌套子类的G型分布，并成功地作出了一个新的改进类的无限可分分布。