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Deterministic representation for position-dependent random maps

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posted on 01.09.2017, 10:27 by Wael BahsounWael Bahsoun, Christopher Bose, Anthony Quas
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 corresponding to eigenvalues of unit modulus for the Frobenius-Perron (transfer) operator of the random map and for those 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Discrete and Continuous Dynamical Systems

Volume

22

Issue

3

Pages

529 - 540

Citation

BAHSOUN, W., BOSE, C. and QUAS, A., 2008. Deterministic representation for position-dependent random maps. Discrete and Continuous Dynamical Systems. Series A, 22 (3), pp.529-540.

Publisher

© American Institute of Mathematical Sciences

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2008

Notes

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems, Series A following peer review. The definitive publisher-authenticated version, BAHSOUN, W., BOSE, C. and QUAS, A., 2008. Deterministic representation for position-dependent random maps. Discrete and Continuous Dynamical Systems. Series A, 22 (3), pp.529-540, is available online at: https://doi.org/10.3934/dcds.2008.22.529.

ISSN

1078-0947

eISSN

1553-5231

Language

en

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