Passage time and fluctuation calculations for subexponential Levy processes

被引:2
|
作者
Doney, Ron [1 ]
Klueppelberg, Claudia [2 ]
Maller, Ross [3 ]
机构
[1] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England
[2] Tech Univ Munich, Ctr Math Sci, Boltzmannstr 3, D-85748 Garching, Germany
[3] Australian Natl Univ, Res Sch Finance Actuarial Studies & Appl Stat, GPO Box 4, Canberra, ACT 0200, Australia
基金
澳大利亚研究理事会;
关键词
fluctuation theory; Levy process; maximum domain of attraction; overshoot; passage time; regular variation; subexponential growth; undershoot; CONVOLUTION EQUIVALENCE; ATTRACTION; OVERSHOOTS;
D O I
10.3150/15-BEJ700
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 consider the passage time problem for Levy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to -infinity a.s. of the process, possibly at a linear rate (the finite mean case), but possibly much faster (the infinite mean case), together with subexponential growth on the positive side. Local and functional versions of limit distributions are derived for the passage time itself, as well as for the position of the process just prior to passage, and the overshoot of a high level. A significant connection is made with extreme value theory via regular variation or maximum domain of attraction conditions imposed on the positive tail of the canonical measure, which are shown to be necessary for the kind of convergence behaviour we are interested in.
引用
收藏
页码:1491 / 1519
页数:29
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