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

无限可分过程和无限可分分布若干问题的研究

• 批准号: 19340025
• 负责人: MAEJIMA Makoto
• 金额: $ 5.16万
• 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: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340025/
• 关键词: 無限分解可能過程; 無限分解可能分布; レヴィ過程; レヴィ測度; オルンシュタイン・ウーレンベック過程; α-自己分解可能分布; 国際研究者交流; スイス:メキシコ:フランス; フラクショナルレヴィ過程; 自由確率論; メキシコ、シンガポール; メキシコ:台湾

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.

无限可分分布的子类被表征为关于Levy过程的随机积分映射的范围。有一种猜想，这种映射迭代得到的极限类与许多映射的稳定分布类的闭包相同。我们成功地证明了这个猜想是正确的。此外，我们还解决了一个长期未解决的问题，即半自分解分布的随机积分映射与Levy过程的刻画。除此之外，我们还解决了许多相关问题，并为进一步的研究发现了许多新的思路。

项目成果

Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators

• DOI: 10.1016/j.ffa.2008.03.001
• 发表时间: 2008-11
• 期刊: Finite Fields Their Appl.
• 作者: V. Berthé;H. Nakada;Rie Natsui

α-連分数変換から作られる確率過程の1-parameter familyのentropyの変化について

关于由 α 连分数变换创建的 1 参数族随机过程的熵变化

• 发表时间: 2007
• 作者: 夏井利恵;仲田均
• 通讯作者: 仲田均

Subclass of Goldie-Steutel-Bondesson class of infinitely divisible distributions on R^d by Upsilon-mapping

R^d 上 Upsilon 映射的无限可分分布 Goldie-Steutel-Bondesson 类的子类

• 发表时间: 2007
• 期刊: ALEA 3
• 作者: 大川 鉄平;角 洋一;N. Hayashi and P. I. Naumkin;M. Maejima
• 通讯作者: M. Maejima

Limit theorems for weighted sums of infinite variance random variables attracted to integrals of linear fractional stable motions

线性分数稳定运动积分所吸引的无限方差随机变量的加权和的极限定理

• 发表时间: 2008
• 期刊: Tokyo J. Math. 31
• 作者: M. Maejima;S. Suzuki
• 通讯作者: S. Suzuki

The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions

几类无限可分分布的嵌套子类的极限与稳定分布类的闭包相同

• 发表时间: 2009
• 期刊: Probab.Th.Relat.Fields 145
• 作者: K. Kajiwara;et. al.;大塚厚二;Y.Ohta;大塚 厚二;Kumi Yasuda;Hideyuki Azegami;N. Hayashi and P. I. Naumkin;Y. Ohta;N. Hayashi and P. I. Naumkin;Makoto Maejima
• 通讯作者: Makoto Maejima