Point processes associated with stationary stable processes

[摘要] Point processes induced by stationary symmetric alpha-stable (SalphaS) processes can have diverse behavior. We distinguish two cases, depending on whether the stationary SalphaS process is governed by a dissipative or conservative flow. In the case of dissipative flows, the process is a mixed moving average and the family of scaled point processes converge to a Poisson cluster process. In the case of a conservative flow, we give two examples showing how diverse the behavior can be. (C) 2004 Elsevier B.V. All rights reserved.

[发布日期] 2004-12-01

[关键词] stationary process;stable process;point process;weak convergence;vague convergence;random measure