ON HITTING TIMES FOR JUMP-DIFFUSION PROCESSES WITH PAST DEPENDENT LOCAL CHARACTERISTICS

被引：7
作者：
SCHAL, M
机构：
[1] Institut für Angewandte Mathematik, Universität Bonn
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1993年 / 47卷 / 01期
关键词：
HITTING TIMES; LAPLACE TRANSFORM; EXPECTATION AND VARIANCE; MARTINGALES; DIFFUSIONS; COMPOUND POISSON PROCESS; RANDOM WALKS; M/G/1; QUEUE; PERTURBATION; CONTROL;
D O I：
10.1016/0304-4149(93)90099-P
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：
It is well known how to apply a martingale argument to obtain the Laplace transform of the hitting time of zero (say) for certain processes starting at a positive level and being skip-free downwards. These processes have stationary and independent increments. In the present paper the method is extended to a more general class of processes the increments of which may depend both on time and past history. As a result a generalized Laplace transform is obtained which can be used to derive sharp bounds for the mean and the variance of the hitting time. The bounds also solve the control problem of how to minimize or maximize the expected time to reach zero.
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页码：131 / 142
页数：12
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