Weak convergence of subordinators to extremal processes

Offer Kella and Andreas Löpker

Stochastic Processes and their Applications, 2013, vol. 123, issue 8, 3122-3131

Abstract: For certain subordinators (Xt)t≥0 it is shown that the process (−tlogXts)s>0 tends to an extremal process (η̂s)s>0 in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that (z∧(−tlogXts))s≥0 converges weakly to (z∧η̂s)s≥0 in D[0,∞), the space of càdlàg functions equipped with Skorohod’s J1 metric.

Keywords: Lévy process; Subordinator; Extremal process; Small-time convergence (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2013.03.010

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