Weak convergence of subordinators to extremal processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Kella, Offer¹  Loepker, Andreas² 

[1] Hebrew Univ Jerusalem, Dept Stat, IL-91905 Jerusalem, Israel

[2] Univ Hamburg, Dept Econ & Social Sci, D-22043 Hamburg, Germany

关键词: Levy process;    Subordinator;    Extremal process;    Small-time convergence;   

DOI  :  10.1016/j.spa.2013.03.010

来源: Elsevier

【 摘 要 】

For certain subordinators (X-t)(t >= 0) it is shown that the process (-t log X-ts)(s>0) tends to an extremal process ((eta)over cap(s))(s>0) in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that (z boolean AND(-t log X-ts))(s >= 0) converges weakly to (z boolean AND<^>(eta)over cap(s))(s >= 0) in D[0, infinity), the space of cadlag functions equipped with Skorohod's J(1) metric. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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