On extrema of stable processes.
On extrema of stable processes.
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关于稳定过程的极值。
DOI：
10.1214/10-aop577
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发表时间：
2010
影响因子：
2.3
通讯作者：
A. Kuznetsov
中科院分区：
文献类型：
--
作者：
A. Kuznetsov
我们研究Wiener-HOPF分解和超级稳定过程的极端分布。通过将Wiener-HOPF因子与一定的椭圆形函数联系起来，我们能够获得许多明确和一般的结果，例如无限的串联表示和渐近扩展超级的密度，Wiener-Hopf因子和wiener-hopf因子和渐变表达式这些功能的梅林蛋白转换，准周期性和功能身份，在某些特殊情况下有限的产物表示和最高功能满足的分布中的有限产品表示。
We study the Wiener--Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener--Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such as infinite series representations and asymptotic expansions for the density of supremum, explicit expressions for the Wiener--Hopf factors and the Mellin transform of the supremum, quasi-periodicity and functional identities for these functions, finite product representations in some special cases and identities in distribution satisfied by the supremum functional.