For BM, there is a downcrossing representation of the local time at 0. Namely, $L_t(0)=\lim_2 (b_i-a_i)D(a_i,b_i,t)$, where $D$ is the number of downcrossing between level $b_i$ and $a_i$.
I am wondering whether there is a similar representation for local time of fBm using downcrossing. I only found some results for stationary gaussian process and semi-martingales. But for fBm, it doesn't work. I tried to mimic the proof for BM, but due to the dependence of the increase of fBm, I am stuck. Could anyone please give me any hint about this? Or how is the research going for this problem? It will be greatly appreciated.