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Fractal sets determined by dilation-stable processes

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  • Hou, Yanyan
  • Ying, Jiangang
  • Dai, Chaoshou

Abstract

Let X={X(t),t∈R+} be a dilation-stable process on Rd. We determine a Hausdorff measure function ϕ(a) such that the fractal set X[0,1]={X(t):0⩽t⩽1} has positive finite ϕ-measure. We also investigate the packing measure of X[0,1].

Suggested Citation

  • Hou, Yanyan & Ying, Jiangang & Dai, Chaoshou, 2008. "Fractal sets determined by dilation-stable processes," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 852-863.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:3:p:852-863
    DOI: 10.1016/j.chaos.2007.01.040
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Xiao, Yimin, 2005. "Dimension results for sample paths of operator stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 55-75, January.
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