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Seminar on Probability and Statistics Wednesday February 4 2009 Tokyo 128 1:40-2:50 pm
Applications of Iterated Function Systems to Inference and Simulation
Stefano Maria Iacus Universita degli Studi di Milano Abstract The Iterated Function Systems (IFSs) were born in mid eighties as
applications of the theory of discrete dynamical systems and as useful
tools for buildings fractals and other similar sets or to produce
image compression algorithms.
The fundamental result on which the IFS method is based is the
Banach contraction theorem because IFSs are defined as operators with
some contractive property.
In practical applications the crucial point is to solve the inverse
problem: given an element f in some metric space (S,d), find a
contraction T:S -> S that admits a unique fixed point p such that
d(f,p)< eps. When eps=0 the inverse problem is solved exactly and the
fixed point p can be identified with the operator T, but in most
cases T is an approximation of the target f and T takes linear forms.
We present applications of the IFS technique to the problem of
estimation of distribution and density functions and to the simulation
of L2 stochastic processes.
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