Article

# SRB Measures For Certain Markov Processes

07/2009; DOI:abs/0907.3372
Source: arXiv

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.

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8 Dec 2012

### Keywords

constituent maps

ergodic invariant measures $\delta_0$

iterated function systems

SRB

SRB measures

sufficient conditions

theorems

upper