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Hausdorff dimension theorems for self-similar Markov processes

Liu Luqin, Xiao Yimin

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 2

369--383

Let X(t) (t ∈R+) be an α-self-similar Markov process on Rd or Rd+. The Hausdorff dimension of the image, graph and zero set of X (t) are obtained under certain mild conditions. Similar results are also proved for a class of elliptic diffusions.