In this article, we obtain sharp conditions for the existence of the high order derivatives (k-th order) of intersection local time α (k) (0) of two independent d-dimensional fractional Brownian motions B H 1 t and B H 2 s with Hurst parameters H1 and H2, respectively. We also study their exponential integrability.
In this article, existence of the k-th order derivatives of local time α (k) (x, t) is considered for two d-dimensional fractional Ornstein-Uhlenbeck processes X H 1 t and X H 2 s with Hurst parameters H1 and H2, respectively. Moreover, Hôlder regularity condition of fractional Ornstein-Uhlenbeck process X H t of local time α(k) (x, t) is obtained by some techniques using in Guo et al. (2017) and in Lou et al. (2017).
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