SRB measures for certain Markov processes

Wael Bahsoun; Paweł Góra

doi:10.3934/dcds.2011.30.17

Article Contents

2011, Volume 30, Issue 1: 17-37. Doi: 10.3934/dcds.2011.30.17

This issue Previous Article Recurrence for random dynamical systems Next Article Existence of solutions for a Boussinesq system on the half line and on a finite interval

SRB measures for certain Markov processes

Wael Bahsoun^1, and
Paweł Góra^2,

1.
Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU
2.
Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, H3G 1M8

Received: December 31, 2009

Revised: June 30, 2010

Published: December 2010

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Abstract

We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then, when all the constituent maps have common fixed points at 0 and 1, theorems are given to analyze properties of the ergodic invariant measures $\delta_0$ and $\delta_1$. In particular, sufficient conditions for $\delta_0$ and/or $\delta_1$ to be, or not to be, SRB measures are given. We apply some of our results to asset market games.

Keywords:

Iterated Function System,
SRB-Measures.

Mathematics Subject Classification: Primary 37A05, 37E05, 37H99.

Citation:

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