It seems strange but, even after consulting several books, and hours spent on google, nothing came out about a law of iterated logarithm for the fractional Brownian motion. I just need a precise reference, on where I can find such a law. Thanks. **EDIT:** My goal is to prove that the fractional Brownian motion of hurst parameter $0<H<1$ has not $H$-Holder continuous trajectories; for the standard BM this can be done in a few lines by exploiting the "standard LIL"; thus, I thought in the fractional case, this can be done in a similar way.