Higher-order derivatives of self-intersection local time for linear fractional stable processes

Abstract

In this paper, we aim to consider the k = (k1, k2,..., kd)-th order derivatives ?(k)(T, x) of selfintersection local time ?(T, x) for the linear fractional stable process X?,H in Rd with indices ? ? (0, 2) and H = (H1,...,Hd) ? (0, 1)d. We first give sufficient condition for the existence and joint H?lder continuity of the derivatives ?(k)(T, x) using the local nondeterminism of linear fractional stable processes. As a related problem, we also study the power variation of ?(k)(T, x).