On a theorem in multi-parameter potential theory

Ming Yang (Department of Mathematics, University of Illinois, Urbana, IL 61801)

Abstract


We prove that the expected Lebesgue measure of the range of an additive Levy process is positive if and only if the product $\Re([1+\Psi_1(\xi)]^{-1})...\Re([1+\Psi_N(\xi)]^{-1})$ is integrable. This was previously proved by Khoshnevisan, Xiao and Zhong [1] under a sector condition.

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Pages: 267-275

Publication Date: September 5, 2007

DOI: 10.1214/ECP.v12-1293

References

  1. Khoshnevisan, Davar; Xiao, Yimin; Zhong, Yuquan. Measuring the range of an additive Lévy process. Ann. Probab. 31 (2003), no. 2, 1097--1141. MR1964960 (2004c:60155)
  2. D. Khoshnevisan, N.-R. Sheih, and Y. Xiao, Hausdorff dimension of the contours of symmetric additive proceeses, Probab. Th. Rel. Fields (2006), to appear.
  3. Mattila, Pertti. Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability. Cambridge Studies in Advanced Mathematics, 44. Cambridge University Press, Cambridge, 1995. xii+343 pp. ISBN: 0-521-46576-1; 0-521-65595-1 MR1333890 (96h:28006)
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