SRB Measures For Certain Markov Processes

2009/07/20 by Wael Bahsoun, Bahsoun, Wael, Paweł Góra +2
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Dynamics and Fractals #Probability (math.PR) #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.0907.3372

openalex publication_date 2009/07/20 · arxiv created 2009/12/30 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 δ₀ and δ₁. In particular, sufficient conditions for δ₀ and/or δ₁ to be, or not to be, SRB measures are given. We apply some of our results to asset market games.

Citations

• Random dynamical systems

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