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Semi-Markov Models and Motion in Heterogeneous Media

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Abstract

In this paper we study continuous time random walks such that the holding time in each state has a distribution depending on the state itself. For such processes, we provide integro-differential (backward and forward) equations of Volterra type, exhibiting a position dependent convolution kernel. Particular attention is devoted to the case where the holding times have a power-law decaying density, whose exponent depends on the state itself, which leads to variable order fractional equations. A suitable limit yields a variable order fractional heat equation, which models anomalous diffusions in heterogeneous media.

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Authors and Affiliations

  1. Dipartimento di Scienze Statistiche, Sapienza - Università di Roma, Rome, Italy

    Costantino Ricciuti

  2. Dipartimento di Matematica e applicazioni “Renato Caccioppoli”, Università degli studi di Napoli “Federico II”, Naples, Italy

    Bruno Toaldo

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  1. Costantino Ricciuti
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  2. Bruno Toaldo
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Correspondence to Costantino Ricciuti.

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Ricciuti, C., Toaldo, B. Semi-Markov Models and Motion in Heterogeneous Media. J Stat Phys 169, 340–361 (2017). https://doi.org/10.1007/s10955-017-1871-2

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  • DOI: https://doi.org/10.1007/s10955-017-1871-2

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