ITERATED FUNCTION SYSTEMS WITH PLACE-DEPENDENT PROBABILITIES AND THE INVERSE PROBLEM OF MEASURE APPROXIMATION USING MOMENTS

Abstract

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.