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The Hausdorff α-dimensional measures of the level sets and the graph of theN-parameter Wiener process

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LetW (N,d) be theN-parameter Wiener process with values inR d. Then the dimension of the level sets isN−d/2 with positive probability ifd<2N. The dimension of the graph is a.s. min {2N,N+d/2}. The level sets have zero (N−d/2)-measure a.s. and the graph has zero min {2N,N+d/2}-measure a.s.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    M. L. Puri & L. T. Tran

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  1. M. L. Puri
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  2. L. T. Tran
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Research supported by the Air Force Office of Scientific Research AFSC, USAF, under Grant No. AFORS 76-2927. Reproduction in whole or part is permitted for any purpose of the U.S. Government.

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Puri, M.L., Tran, L.T. The Hausdorff α-dimensional measures of the level sets and the graph of theN-parameter Wiener process. Metrika 31, 275–283 (1984). https://doi.org/10.1007/BF01915212

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  • DOI: https://doi.org/10.1007/BF01915212

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