Deterministic representations for position dependent random maps
Date
2010-02-19T22:49:10Z
Authors
Bahsoun, Wael
Bose, Christopher
Quas, Anthony
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Abstract
We give a deterministic representation for position dependent random maps and describe the structure of its set of invariant measures. Our construction generalizes the skew product representation of random maps with constant probabilities. In particular, we establish one-to-one correspondence between eigenfunctions of the Frobenius-Perron (transfer) operator for the random map and that of the skew. An immediate consequence is one-to-one correspondence between absolutely continuous invariant measures (acims) for the position dependent random map and acims for its deterministic representation.
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Keywords
random map, skew product, absolutely continuous invariant measure, technical reports (mathematics and statistics)