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Computing invariant measures of piecewise convex transformations

Abstract

LetS:[0, 1]→[0,1] be a piecewise convex transformation satisfying some conditions which guarantee the existence of an absolutely continuous invariant probability measure. We prove the convergence of a class of Markov finite approximations for computing the invariant measure, using a compactness argument forL 1-spaces.

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Research was supported in part by a grant from the Minority Scholars Program through the University of Southern Mississippi.

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Ding, J. Computing invariant measures of piecewise convex transformations. J Stat Phys 83, 623–635 (1996). https://doi.org/10.1007/BF02183742

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Key Words

  • Invariant measure
  • Frobenius-Perron operator