Summary
The paper obtains bounds on the Hausdorff and packing measures of the imageX(E) of a Borel setE by a transient strictly stable processX t which a.s. hold for allE and for every measure function\(h_{\beta ,\gamma } (s) = s^\beta \left| {\log s} \right|^{\gamma ^ \star }\). In some cases examples are constructed to show that the bounds are sharp.
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While preparing this paper, the author was partially supported by NSERC and by NSF on contract #DMS-8317815
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Perkins, E.A., Taylor, S.J. Uniform measure results for the image of subsets under Brownian motion. Probab. Th. Rel. Fields 76, 257–289 (1987). https://doi.org/10.1007/BF01297485
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DOI: https://doi.org/10.1007/BF01297485