Multiple Points of Operator Semistable Lévy Processes
We determine the Hausdorff dimension of the set 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 resul...
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| Veröffentlicht in: | Journal of theoretical probability 2020-03, Vol.33 (1), p.153-179 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We determine the Hausdorff dimension of the set 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 (Luks and Xiao in J Theor Probab 30(1):297–325,
2017
) where the set of double points
(
k
=
2
)
was studied in the symmetric operator stable case. |
|---|---|
| ISSN: | 0894-9840 1572-9230 |
| DOI: | 10.1007/s10959-018-0859-4 |