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Fractional Dynamics at Multiple Times

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Abstract

A continuous time random walk (CTRW) imposes a random waiting time between random particle jumps. CTRW limit densities solve a fractional Fokker-Planck equation, but since the CTRW limit is not Markovian, this is not sufficient to characterize the process. This paper applies continuum renewal theory to restore the Markov property on an expanded state space, and compute the joint CTRW limit density at multiple times.

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Authors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, USA

    Mark M. Meerschaert

  2. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    Peter Straka

Authors
  1. Mark M. Meerschaert
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  2. Peter Straka
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Corresponding author

Correspondence to Mark M. Meerschaert.

Additional information

This research was partially supported by NSF grants DMS-1025486, DMS-0803360, and NIH grant R01-EB012079.

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Meerschaert, M.M., Straka, P. Fractional Dynamics at Multiple Times. J Stat Phys 149, 878–886 (2012). https://doi.org/10.1007/s10955-012-0638-z

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  • DOI: https://doi.org/10.1007/s10955-012-0638-z

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