approximation of probability measures
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Fractals ◽  
2018 ◽  
Vol 26 (05) ◽  
pp. 1850076 ◽  
Author(s):  
D. LA TORRE ◽  
E. MAKI ◽  
F. MENDIVIL ◽  
E. R. VRSCAY

We are concerned with the approximation of probability measures on a compact metric space [Formula: see text] by invariant measures of iterated function systems with place-dependent probabilities (IFSPDPs). The approximation is performed by moment matching. Associated with an IFSPDP is a linear operator [Formula: see text], where [Formula: see text] denotes the set of all infinite moment vectors of probability measures on [Formula: see text]. Let [Formula: see text] be a probability measure that we desire to approximate, with moment vector [Formula: see text]. We then look for an IFSPDP which maps [Formula: see text] as close to itself as possible in terms of an appropriate metric on [Formula: see text]. Some computational results are presented.


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