On a class of characterization problems for random convex combinations

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Ludwig Baringhaus
  • Rudolf Grübel

Organisationseinheiten

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)555-567
Seitenumfang13
FachzeitschriftAnnals of the Institute of Statistical Mathematics
Jahrgang49
Ausgabenummer3
PublikationsstatusVeröffentlicht - Sept. 1997

Abstract

We consider stochastic equations of the form X =d W1X + W2X′, where (W1, W2), X and X′ are independent, '=d' denotes equality in distribution, EW1 + EW2 = 1 and X =d X′. We discuss existence, uniqueness and stability of the solutions, using contraction arguments and an approach based on moments. The case of {0, 1}-valued W1 and constant W2 leads to a characterization of exponential distributions.

ASJC Scopus Sachgebiete

Zitieren

On a class of characterization problems for random convex combinations. / Baringhaus, Ludwig; Grübel, Rudolf.
in: Annals of the Institute of Statistical Mathematics, Jahrgang 49, Nr. 3, 09.1997, S. 555-567.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Baringhaus L, Grübel R. On a class of characterization problems for random convex combinations. Annals of the Institute of Statistical Mathematics. 1997 Sep;49(3):555-567. doi: 10.1023/A:1003127114209
Baringhaus, Ludwig ; Grübel, Rudolf. / On a class of characterization problems for random convex combinations. in: Annals of the Institute of Statistical Mathematics. 1997 ; Jahrgang 49, Nr. 3. S. 555-567.
Download
@article{72007e1c68cd4d6e9523e352d35e969f,
title = "On a class of characterization problems for random convex combinations",
abstract = "We consider stochastic equations of the form X =d W1X + W2X′, where (W1, W2), X and X′ are independent, '=d' denotes equality in distribution, EW1 + EW2 = 1 and X =d X′. We discuss existence, uniqueness and stability of the solutions, using contraction arguments and an approach based on moments. The case of {0, 1}-valued W1 and constant W2 leads to a characterization of exponential distributions.",
keywords = "Characterization problems, Contractions, Exponential distributions, Stochastic difference equations",
author = "Ludwig Baringhaus and Rudolf Gr{\"u}bel",
year = "1997",
month = sep,
doi = "10.1023/A:1003127114209",
language = "English",
volume = "49",
pages = "555--567",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer Netherlands",
number = "3",

}

Download

TY - JOUR

T1 - On a class of characterization problems for random convex combinations

AU - Baringhaus, Ludwig

AU - Grübel, Rudolf

PY - 1997/9

Y1 - 1997/9

N2 - We consider stochastic equations of the form X =d W1X + W2X′, where (W1, W2), X and X′ are independent, '=d' denotes equality in distribution, EW1 + EW2 = 1 and X =d X′. We discuss existence, uniqueness and stability of the solutions, using contraction arguments and an approach based on moments. The case of {0, 1}-valued W1 and constant W2 leads to a characterization of exponential distributions.

AB - We consider stochastic equations of the form X =d W1X + W2X′, where (W1, W2), X and X′ are independent, '=d' denotes equality in distribution, EW1 + EW2 = 1 and X =d X′. We discuss existence, uniqueness and stability of the solutions, using contraction arguments and an approach based on moments. The case of {0, 1}-valued W1 and constant W2 leads to a characterization of exponential distributions.

KW - Characterization problems

KW - Contractions

KW - Exponential distributions

KW - Stochastic difference equations

UR - http://www.scopus.com/inward/record.url?scp=9844243443&partnerID=8YFLogxK

U2 - 10.1023/A:1003127114209

DO - 10.1023/A:1003127114209

M3 - Article

AN - SCOPUS:9844243443

VL - 49

SP - 555

EP - 567

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 3

ER -