Random fractals and probability metrics (Q2713148)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Random fractals and probability metrics |
scientific article |
Statements
Random fractals and probability metrics (English)
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21 April 2002
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random measure
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fractal
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self-similar
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probability metric
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random fractal
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Monge-Kantorovich metric
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scaling operator
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iterated function system
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minimal metric
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0.92623764
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New existence, uniqueness and convergence results for self-similar random measures are shown. In particular, self-similar random measures with non-constant total mass are treated extensively. The methods of this paper allow to work under very general conditions on the random iterated function systems. The principal tools are various modifications of the contraction method. The method is exploited by intricate choices of metrics on spaces of random measures and their distributions. The contraction properties of these metrics arise from the linear structure of the set of measures rather than any independence properties. In order to establish almost sure convergence results and to deal with the case of non-constant mass the scaling operators are extended to a space of construction trees.
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