Geodesic
Higher-order derivatives of self-intersection local time for linear fractional stable processes
Filomat, Tome 37 (2023) no. 27, p. 9169

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DOI

In this paper, we aim to consider the k = (k 1 , k 2 , · · · , k d)-th order derivatives β (k) (T, x) of self-intersection local time β(T, x) for the linear fractional stable process X α,H in R d with indices α ∈ (0, 2) and H = (H 1 , · · · , H d) ∈ (0, 1) d. We first give sufficient condition for the existence and joint H ¨ older continuity of the derivatives β (k) (T, x) using the local nondeterminism of linear fractional stable processes. As a related problem, we also study the power variation of β (k) (T, x).
DOI : 10.2298/FIL2327169Z
Classification : 60G52, 60J55
Keywords: Linear fractional stable process, self-intersection local time, joint Hölder continuity, power variation 
Huan Zhou; Guangjun Shen; Qian Yu. Higher-order derivatives of self-intersection local time for linear fractional stable processes. Filomat, Tome 37 (2023) no. 27, p. 9169 . doi: 10.2298/FIL2327169Z
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     title = {Higher-order derivatives of self-intersection local time for linear fractional stable processes},
     journal = {Filomat},
     pages = {9169 },
     year = {2023},
     volume = {37},
     number = {27},
     doi = {10.2298/FIL2327169Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2327169Z/}
}
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