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Fractal dimension results for continuous time random walks

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  • Meerschaert, Mark M.
  • Nane, Erkan
  • Xiao, Yimin

Abstract

Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion.

Suggested Citation

  • Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1083-1093
    DOI: 10.1016/j.spl.2013.01.001
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2009. "Correlated continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1194-1202, May.
    2. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    3. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2006. "Stochastic model for ultraslow diffusion," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1215-1235, September.
    4. Meerschaert, Mark M. & Scalas, Enrico, 2006. "Coupled continuous time random walks in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 114-118.
    5. Veillette, Mark & Taqqu, Murad S., 2010. "Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 697-705, April.
    6. Straka, P. & Henry, B.I., 2011. "Lagging and leading coupled continuous time random walks, renewal times and their joint limits," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 324-336, February.
    7. Davydov, Yu., 2012. "On convex hull of d-dimensional fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 37-39.
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    Cited by:

    1. Asogwa, Sunday A. & Nane, Erkan, 2017. "Intermittency fronts for space-time fractional stochastic partial differential equations in (d+1) dimensions," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1354-1374.
    2. Mijena, Jebessa B. & Nane, Erkan, 2015. "Space–time fractional stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3301-3326.

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