Studies on several problems on infinitely divisible processes and infinitely divisible distributions

无限可分分布的子类被刻画为关于Levy过程的随机积分映射的范围。有一个猜想，这种映射的迭代得到的极限类与许多映射的稳定分布类的闭包是相同的。我们成功地证明了这个猜想是正确的。进一步地，我们解决了一个长期没有解决的问题，即用一个带有Levy过程的随机积分映射刻画半自可分解分布。除此之外，我们还解决了许多相关问题，为进一步的研究找到了新的思路。

Subclasses of infinitely divisible distributions are characterized as ranges of stochastic integral mappings with respect to Levy processes. There was a conjecture that the limiting classes obtained by the iteration of such mappings are identical to the closure of the class of stable distributions for many mappings. We succeeded to show that the conjecture is true. Further, we solved one problem unsolved for long time that is a characterization of semi-selfdecomposable distribution by a stochastic integral mapping with Levy processes. In addition to those, we solved many related problems and found many new ideas for the further studies.