On the small-time behavior of subordinators

Shaul K. Bar-Lev, Andreas Löpker, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


We prove several results on the behavior near t = 0 of Y-t t for certain (0,∞)-valued stochastic processes (Y t)t>0. In particular, we show for Lévy subordinators that the Pareto law on [1,∞) is the only possible weak limit and provide necessary and sufficient conditions for the convergence. More generally, we also consider the weak convergence of tL(Yt) as t →0 for a decreasing function L that is slowly varying at zero. Various examples demonstrating the applicability of the results are presented.

Original languageEnglish
Pages (from-to)823-835
Number of pages13
Issue number3
StatePublished - Aug 2012


  • Pareto law
  • Regular variation
  • Subordinator
  • Weak limit theorem

ASJC Scopus subject areas

  • Statistics and Probability


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