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Medientyp:
E-Artikel
Titel:
A GENERALIZATION OF IFS WITH PROBABILITIES TO INFINITELY MANY MAPS
Beteiligte:
MENDIVIL, FRANKLIN
Erschienen:
The Rocky Mountain Mathematics Consortium, 1998
Erschienen in:The Rocky Mountain Journal of Mathematics
Sprache:
Englisch
ISSN:
0035-7596;
1945-3795
Entstehung:
Anmerkungen:
Beschreibung:
<p>This paper considers the problem of extending the notion of an IFS with probabilities from the case of finitely many maps in the IFS to the case of infinitely many maps. We prove that, under an average contractivity condition, the IFS is contractive in the Monge-Kantorovich metric. We also show that the invariant distribution is continuous with respect to the parameters of the IFS. Furthermore, using results of Lewellen, we obtain a result relating the support of the invariant measure to the attractor of the "geometric" IFS. Finally, we discuss the issue of the convergence of integrals With respect to the invariant measure and estimates on the error of these integrals.</p>