Weak convergence of subordinators to extremal processes

Offer Kella*, Andreas Löpker

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For certain subordinators (Xt)t≥0 it is shown that the process (-tlogXts)s>0 tends to an extremal process (ηîs)s>0 in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that ((-tlog X ts))s≥0 converges weakly to (Z,ns) s≥0 in D[0,∞), the space of càdl̀ag functions equipped with Skorohod's J1 metric.

Original languageAmerican English
Pages (from-to)3122-3131
Number of pages10
JournalStochastic Processes and their Applications
Volume123
Issue number8
DOIs
StatePublished - 2013

Bibliographical note

Funding Information:
The authors thank Shaul Bar Lev and Thomas Kurtz for useful discussions. The first author was supported in part by grant No. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics.

Keywords

  • Extremal process
  • Lévy process
  • Small-time convergence
  • Subordinator

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