ON EXTREMA OF STABLE PROCESSES

• 成果类型: Article
• 署名作者: Kuznetsov, Alexey
• 署名单位: York University - Canada
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP577
• 发表日期: 2011
• 页码: 1027-1060
• 关键词: wiener-hopf factorization; double-gamma-function; no negative jumps; Levy processes; supremum; time; LAW

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.