On a zero-crossing probability |
| |
Authors: | Colin L Mallows Vijayan N Nair |
| |
Institution: | (1) AT&T Bell Laboratories, 07974 Murray Hill, NJ, U.S.A. |
| |
Abstract: | Let {X(t), 0} be a compound Poisson process so that E{exp (–sX(t))}=exp (–t (s)), where (s)= (1– (s)), is the intensity of the Poisson process, and (s) is the Laplace transform of the distribution of nonnegative jumps. Consider the zero-crossing probability =P{X(t)–t=0 for some t,0<t< }. We show that =![PHgr](/content/x40475t200211868/xxlarge934.gif) ( ) where is the largest nonnegative root of the equation (s)=s. It is conjectured that this result holds more generally for any stochastic process with stationary independent increments and with sample paths that are nondecreasing step functions vanishing at 0. |
| |
Keywords: | Ballot theorem compound Poisson process |
本文献已被 SpringerLink 等数据库收录! |
|