Details
| Original language | English |
|---|---|
| Pages (from-to) | 555-567 |
| Number of pages | 13 |
| Journal | Annals of the Institute of Statistical Mathematics |
| Volume | 49 |
| Issue number | 3 |
| Publication status | Published - 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.
Keywords
- Characterization problems, Contractions, Exponential distributions, Stochastic difference equations
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
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In: Annals of the Institute of Statistical Mathematics, Vol. 49, No. 3, 09.1997, p. 555-567.
Research output: Contribution to journal › Article › Research › peer review
}
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 -