具有平稳增量的自相似过程的边缘分布

数学物理学报 ›› 2003, Vol. 23 ›› Issue (1): 84-90.

具有平稳增量的自相似过程的边缘分布

钱能生

五邑大学数学物理系

出版日期:2003-02-25 发布日期:2003-02-25
基金资助:
国家自然科学基金资助课题

On Marginal Distribution of SelfSimilar\=Processes with Stationary Increments

JIAN Nai-Sheng

Online:2003-02-25 Published:2003-02-25
Supported by:
国家自然科学基金资助课题

摘要/Abstract

摘要：

设Ｘ＝（Ｘ\-t）\-\{t≥0\} 是指数Ｈ（＞０）型的具有平稳增量的自相似过程，该文给出了Ｘ\-１的边缘分布的一些结果。对于Ｈ≠１，log\++Ｘ\-１的压缩函数有一个只依赖于Ｈ的界；对于Ｈ＞０，Ｘ\-１除了一些平凡的情形外是非原子的；而对于Ｈ＞１，Ｘ\-１的尾分布的下界也给出了；文章的最后对Ｘ\-１的支撑的连通性给予了讨论并给出了一些结果。

关键词: 平稳增量；自相似过程；压缩函数

Abstract:

Let \$X=(X\-t)\-t≥0\$ be a realvalued stochastic process which is selfsimilar with parameter \$H>0\$ and has stationary increments. Several results about themarginal distribution of \$X\-1\$ are given for \$H≠1, \$there is a bound, depending only on \$H\$, on the concentration function of
log\$X\++\-1\$. For all \$H>0,X\-1\$ cannot have any atomsexcept in certain trivial cases. Some lower bounds are given for the tails of the distribution of \$X\-1\$ in case \$H>1.\$ Finally, some results are given concerning the connectedness of the support of \$X\-1.\$

Key words: Stationary increment, Selfsimilar prcesses, Concentration function.

中图分类号:

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钱能生. 具有平稳增量的自相似过程的边缘分布[J]. 数学物理学报, 2003, 23(1): 84-90.

JIAN Nai-Sheng. On Marginal Distribution of SelfSimilar\=Processes with Stationary Increments[J]. Acta mathematica scientia,Series A, 2003, 23(1): 84-90.