Higher-Order Derivative of Intersection Local Time for Two Independent Fractional Brownian Motions

Abstract

In this article, we obtain sharp conditions for the existence of the high-order derivatives (k-th order) of intersection local time $$ \widehat{\alpha }^{(k)}(0)$$ of two independent d-dimensional fractional Brownian motions $$B^{H_1}_t$$ and $$\widetilde{B}^{H_2}_s$$ of Hurst parameters $$H_1$$ and $$H_2$$ , respectively. We also study their exponential integrability.