Extremal Processes
نویسندگان
چکیده
منابع مشابه
Extremal Theory for Stochastic Processes
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Convergence of a sequence of deterministic functions in the Skorohod topology d 0;? implies convergence of the jumps. For processes with independent additive increments the ®xed discontinuities converge. In this paper it will be shown that this is not true for processes with independent max-increments. The limit in d 0;? of a sequence of stochastically continuous extremal processes may ha...
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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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Let Nn = {(Tnk,Xnk), k ≥ 1} be a Bernoulli p.p. on Z = (0,∞) × [0,∞). We discuss weak limit theorems for Nn as well as for the associated sum and extremal processes Sn(t) = { ∑ Xnk : Tnk ≤ t} and Yn(t) = {∨Xnk : Tnk ≤ t} on an open subset of Z.
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1964
ISSN: 0003-4851
DOI: 10.1214/aoms/1177700394