Point processes associated with stationary stable processes

Sidney Resnick and Gennady Samorodnitsky

Stochastic Processes and their Applications, 2004, vol. 114, issue 2, 191-209

Abstract: Point processes induced by stationary symmetric [alpha]-stable (S[alpha]S) processes can have diverse behavior. We distinguish two cases, depending on whether the stationary S[alpha]S 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.

Keywords: Stationary; process; Stable; process; Point; process; Weak; convergence; Vague; convergence; Random; measure (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (5)

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