Multiple points of operator semistable Lévy processes

2018/02/09 by Tomasz Luks, Luks, Tomasz, Yimin Xiao +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #math.PR #msc:60G17 #msc:60G51 #msc:60J25 #msc:60J30

paper · pdf · doi:10.48550/arxiv.1802.03303

24 pages, editorial changes, to appear in J. Theoret. Probab

arxiv created 2018/09/05 · arxiv updated 2018/09/06

Abstract

We determine the Hausdorff dimension of k-multiple points for a symmetric operator semistable Lévy process X=\X(t), t∈ℝ₊\ in terms of the eigenvalues of its stability exponent. We also give a necessary and sufficient condition for the existence of k-multiple points. Our results extend to all k≥2 the recent work [23], where the set of double points (k = 2) was studied in the symmetric operator stable case.

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