SRB Measures For Certain Markov Processes

Details SRB Measures For Certain Markov Processes SRB Measures For Certain Markov Processes

2009-07-20

arxiv.org/abs/0907.3372v2

Mathematics

Dynamical Systems

Scientific paper

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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