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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:47

Article

关键词: HITTING TIMES;    LAPLACE TRANSFORM;    EXPECTATION AND VARIANCE;    MARTINGALES;    DIFFUSIONS;    COMPOUND POISSON PROCESS;    RANDOM WALKS;    M/G/1 QUEUE;    PERTURBATION;    CONTROL;   

DOI  :  10.1016/0304-4149(93)90099-P

来源: Elsevier

【 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.

【 授权许可】

Free