Suprema and sojourn times of Levy processes with exponential tails

[摘要] We study the tail behaviour of the supremum of sample paths of Levy process with exponential tail of the Levy measure. Our approach is based on the theory of sojourn times developed by S. Berman. It allows us to compute the value of the limit of the ratio P(sup(0 less than or equal to t less than or equal to 1) X(t) > x)/rho(x, infinity) as x --> infinity, where rho is the Levy measure of the process.

[发布日期] 1997-06-16

[关键词] Levy process;exponential distributions;sojourn times