Unimodality of Hitting Times for Stable Processes

被引：2

作者：

Letemplier, Julien ^{[1
]}

Simon, Thomas ^{[1
,2
]}

机构：

[1] Univ Lille 1, Lab Paul Painleve, Cite Sci, F-59655 Villeneuve Dascq, France

[2] Univ Paris 11, Lab Phys Theor & Modeles Stat, F-91405 Orsay, France

来源：

SEMINAIRE DE PROBABILITES XLVI | 2014年 / 2123卷

关键词：

Hitting time; Kanter random variable; Self-decomposability; Size; bias; Stable Levy process; Unimodality; LEVY PROCESSES; DENSITIES; POINTS;

D O I：

10.1007/978-3-319-11970-0_13

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the hitting times for points of real alpha-stable Levy processes (1 < alpha <= 2) are unimodal random variables. The argument relies on strong unimodality and several recent multiplicative identities in law. In the symmetric case we use a factorization of Yano et al. (Semin Probab XLII: 187-227, 2009), whereas in the completely asymmetric case we apply an identity of the second author (Simon, Stochastics 83( 2):203-214, 2011). The method extends to the general case thanks to a fractional moment evaluation due to Kuznetsov et al. (Electr. J. Probab. 19:30, 1-26, 2014), for which we also provide a short independent proof.

引用

页码：345 / 357

页数：13

共 17 条

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