Measuring the Range of an Additive Lévy Process

  title={Measuring the Range of an Additive L{\'e}vy Process},
  author={Davar Khoshnevisan and Yimin Xiao and YUQUAN ZHONG},
X(t) =∑Nj=1 Xj (tj ), where X1, . . . ,XN are independent Lévy processes in Rd . To cite a typical result of this paper, let us suppose that i denotes the Lévy exponent of Xi for each i = 1, . . . ,N . Then, under certain mild conditions, we show that a necessary and sufficient condition for X(R+ ) to have positive d-dimensional Lebesgue measure is the integrability of the function Rd ξ →∏Nj=1 Re{1 + j (ξ)}−1. This extends a celebrated result of Kesten and of Bretagnolle in the one-parameter… CONTINUE READING

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