A note on the existence of solutions to a stochastic recurrence equation
We provide a characterization of strictly stationary solutions to the stochastic recurrence equation zk = c(eK_I)zK_I + g(ek-1) with Borelmeasurable functions c and g, and independent, identically distributed random variables {£&}. Strictly stationary solutions that are functions of the past, re...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2007
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| Sorozat: | Acta scientiarum mathematicarum
73 No. 3-4 |
| Kulcsszavak: | Matematika, Sztochasztikus rekurziós egyenlet |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16213 |
| Tartalmi kivonat: | We provide a characterization of strictly stationary solutions to the stochastic recurrence equation zk = c(eK_I)zK_I + g(ek-1) with Borelmeasurable functions c and g, and independent, identically distributed random variables {£&}. Strictly stationary solutions that are functions of the past, respectively, of the future exist if and only if the expected value Slog |c(eo)| is negative, respectively, positive. The main result of the paper is to show that there is no solution that is a function of the past or the future if E log jc(eo) | = 0. |
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| Terjedelem/Fizikai jellemzők: | 767-779 |
| ISSN: | 0001-6969 |