Random fractals and Probability metrics
Hutchinson, John; Ruschendorf, Ludger
Description
New metrics are introduced in the space of random measures and are applied, with various modifications of the contraction method, to prove existence and uniqueness results for self-similar random fractal measures. We obtain exponential convergence, both in distribution and almost surely, of an iterative sequence of random measures (defined by means of the scaling operator) to a unique self-similar random measure. The assumptions are quite weak, and correspond to similar conditions in the...[Show more]
dc.contributor.author | Hutchinson, John | |
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dc.contributor.author | Ruschendorf, Ludger | |
dc.date.accessioned | 2015-12-13T23:18:23Z | |
dc.date.available | 2015-12-13T23:18:23Z | |
dc.identifier.issn | 0001-8678 | |
dc.identifier.uri | http://hdl.handle.net/1885/90146 | |
dc.description.abstract | New metrics are introduced in the space of random measures and are applied, with various modifications of the contraction method, to prove existence and uniqueness results for self-similar random fractal measures. We obtain exponential convergence, both in distribution and almost surely, of an iterative sequence of random measures (defined by means of the scaling operator) to a unique self-similar random measure. The assumptions are quite weak, and correspond to similar conditions in the deterministic case. The fixed mass case is handled in a direct way based on regularity properties of the metrics and the properties of a natural probability space. Proving convergence in the random mass case needs additional tools, such as a specially adapted choice of the space of random measures and of the space of probability distributions on measures, the introduction of reweighted sequences of random measures and a comparison technique. | |
dc.publisher | Applied Probability Trust | |
dc.source | Advances in Applied Probability | |
dc.subject | Keywords: Approximation theory; Boundary conditions; Convergence of numerical methods; Fractals; Iterative methods; Probability distributions; Theorem proving; Iterative function system; Minimal metric; Monge-Kantorovich metric; Probability metrics; Random fractals | |
dc.title | Random fractals and Probability metrics | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
local.identifier.citationvolume | 32 | |
dc.date.issued | 2000 | |
local.identifier.absfor | 020204 - Plasma Physics; Fusion Plasmas; Electrical Discharges | |
local.identifier.ariespublication | MigratedxPub20433 | |
local.type.status | Published Version | |
local.contributor.affiliation | Hutchinson, John, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Ruschendorf, Ludger, University of Freiburg | |
local.bibliographicCitation.issue | 4 | |
local.bibliographicCitation.startpage | 925 | |
local.bibliographicCitation.lastpage | 947 | |
dc.date.updated | 2015-12-12T08:56:32Z | |
local.identifier.scopusID | 2-s2.0-0343772976 | |
Collections | ANU Research Publications |
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