Weak Convergence of Subordinators to Extremal Processes
نویسندگان
چکیده
For certain subordinators (Xt)t≥0 it is shown that the process (−t logXts)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 ∧ (−t logXts))s≥0 converges weakly to (z ∧ η̂s)s≥0 in D[0,∞), the space of càdlàg functions equipped with Skorohod’s J1 metric.
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