Hausdorff dimension of the graph of an operator semistable Lévy process

2015/06/01 by Lina Wedrich, Wedrich, Lina
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1506.00615

arxiv created 2015/06/01 · openalex publication_date 2015/06/01 · arxiv updated 2015/06/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let X=\X(t):t≥0\ be an operator semistable Lévy process in ℝ^d with exponent E, where E is an invertible linear operator on ℝ^d. For an arbitrary Borel set B⊆ℝ₊ we interpret the graph Gr_X(B)=\(t,X(t)):t∈ B\ as a semi-selfsimilar process on ℝ^d+1, whose distribution is not full, and calculate the Hausdorff dimension of Gr_X(B) in terms of the real parts of the eigenvalues of the exponent E and the Hausdorff dimension of B.

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