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Pointwise and Renyi Dimensions of an Invariant Measure of Random Dynamical Systems with Jumps

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Abstract

We estimate the lower pointwise dimension and the generalized Renyi dimension of an invariant measure of random dynamical systems with jumps. It is worthwhile to note that the dimensions are a useful tool in studying the Hausdorff dimension of measures and sets. Our model generalizes Markov processes corresponding to iterated function systems and Poisson driven stochastic differential equations. It can be used as a description of many physical and biological phenomena.

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University, ul. Bankowa 14, Katowice, 40-007, Poland

    Katarzyna Horbacz

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  1. Katarzyna Horbacz
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Correspondence to Katarzyna Horbacz.

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AMS Subject Classification (2000): Primary 47A35, secondary 58F30

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Horbacz, K. Pointwise and Renyi Dimensions of an Invariant Measure of Random Dynamical Systems with Jumps. J Stat Phys 122, 1041–1059 (2006). https://doi.org/10.1007/s10955-005-9017-3

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  • DOI: https://doi.org/10.1007/s10955-005-9017-3

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