Weak convergence of subordinators to extremal processes

Offer Kella; Andreas Löpker

doi:10.1016/j.spa.2013.03.010

Weak convergence of subordinators to extremal processes

Offer Kella^*, Andreas Löpker

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

For certain subordinators (X_t)_t≥0 it is shown that the process (-tlogX_ts)_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,n_s) _s≥0 in D[0,∞), the space of càdl̀ag functions equipped with Skorohod's J₁ metric.

Original language	English
Pages (from-to)	3122-3131
Number of pages	10
Journal	Stochastic Processes and their Applications
Volume	123
Issue number	8
DOIs	https://doi.org/10.1016/j.spa.2013.03.010
State	Published - 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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10.1016/j.spa.2013.03.010

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title = "Weak convergence of subordinators to extremal processes",

abstract = "For certain subordinators (Xt)t≥0 it is shown that the process (-tlogXts)s>0 tends to an extremal process (η{\^i}s)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 c{\`a}d{\`l}ag functions equipped with Skorohod's J1 metric.",

keywords = "Extremal process, L{\'e}vy process, Small-time convergence, Subordinator",

author = "Offer Kella and Andreas L{\"o}pker",

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.",

year = "2013",

doi = "10.1016/j.spa.2013.03.010",

language = "אנגלית",

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T1 - Weak convergence of subordinators to extremal processes

AU - Kella, Offer

AU - Löpker, Andreas

N1 - 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.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Extremal process

KW - Lévy process

KW - Small-time convergence

KW - Subordinator

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U2 - 10.1016/j.spa.2013.03.010

DO - 10.1016/j.spa.2013.03.010

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AN - SCOPUS:84877871083

SN - 0304-4149

VL - 123

SP - 3122

EP - 3131

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 8

ER -

Weak convergence of subordinators to extremal processes

Abstract

Bibliographical note

Keywords

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