ON EXTREMA OF STABLE PROCESSES

被引：37

作者：

Kuznetsov, Alexey ^{[1
]}

机构：

[1] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

来源：

ANNALS OF PROBABILITY | 2011年 / 39卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Stable processes; supremum; Wiener-Hopf factorization; Mellin transform; functional equations; elliptic functions; double Gamma function; q-Pochhammer symbol; Clausen function; WIENER-HOPF FACTORIZATION; DOUBLE-GAMMA-FUNCTION; NO NEGATIVE JUMPS; LEVY PROCESSES; SUPREMUM; TIME; LAW;

D O I：

10.1214/10-AOP577

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：1027 / 1060

页数：34

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