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Solving the inverse problem for measures using iterated function systems: a new approach
- Part of
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- Journal:
- Advances in Applied Probability / Volume 27 / Issue 3 / September 1995
- Published online by Cambridge University Press:
- 01 July 2016, pp. 800-820
- Print publication:
- September 1995
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- Article
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We present a systematic method of approximating, to an arbitrary accuracy, a probability measure µ on x = [0,1]q, q
1, with invariant measures for iterated function systems by matching its moments. There are two novel features in our treatment. 1. An infinite set of fixed affine contraction maps on 
, w2, · ·· }, subject to an ‘ϵ-contractivity' condition, is employed. Thus, only an optimization over the associated probabilities pi is required. 2. We prove a collage theorem for moments which reduces the moment matching problem to that of minimizing the collage distance between moment vectors. The minimization procedure is a standard quadratic programming problem in the pi which can be solved in a finite number of steps. Some numerical calculations for the approximation of measures on [0, 1] are presented.
1, with invariant measures for iterated function systems by matching its moments. There are two novel features in our treatment. 1. An infinite set of fixed affine contraction maps on 
, 