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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 26 open journal systems 


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 L'evy 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.


Full text: PDF

Pages: 267-275

Published on: September 5, 2007
Bibliography
  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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Electronic Communications in Probability. ISSN: 1083-589X