Higher-Order Derivative of Self-Intersection Local Time for Fractional Brownian Motion

Abstract

We consider the existence and Hölder continuity conditions for the k-th-order derivatives of self-intersection local time for d-dimensional fractional Brownian motion, where $$k=(k_1,k_2,\ldots , k_d)$$ . Moreover, we show a limit theorem for the critical case with $$H=\frac{2}{3}$$ and $$d=1$$ , which was conjectured by Jung and Markowsky [7].