ASYMPTOTICS FOR THE FIRST PASSAGE TIMES OF LEVY PROCESSES AND RANDOM WALKS

作者：Denisov Denis^*; Shneer Vsevolod

来源：Journal of Applied Probability, 2013, 50(1): 64-84.

• Levy process
• random walk
• busy period
• first passage time
• subexponential distribution
• large deviation
• single-server queue

We study the exact asymptotics for the distribution of the first time, tau(x), a Levy process X-t crosses a fixed negative level -x. We prove that P{tau(x) %26gt; t} V (x)P{X-t %26gt;= 0}/t as t -%26gt; infinity for a certain function V(x). Using known results for the large deviations of random walks, we obtain asymptotics for P{tau(x) %26gt; t} explicitly in both light- and heavy-tailed cases.

• 出版日期2013-3