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On properties of continuous-time random walks with non-Poissonian jump-times

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  • Villarroel, Javier
  • Montero, Miquel

Abstract

The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The case of Erlang distributed times is analyzed in detail. Several concrete examples are considered.

Suggested Citation

  • Villarroel, Javier & Montero, Miquel, 2009. "On properties of continuous-time random walks with non-Poissonian jump-times," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 128-137.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:128-137
    DOI: 10.1016/j.chaos.2008.11.015
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    References listed on IDEAS

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    1. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
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