Let $X$ be a two dimensional fractional brownian motion with Hurst parameter $h<\frac{1}{2}$. In `Notes on the two-dimensional fractional Brownian Motion', the authors state that it is a recurrent process, which I am very conviced of, but that I am not able to prove. Could someone help me with that? Does it fall into a general framework for which recurrence is automatic?
Actually, I would need a quantization of the recurrence. Basically, let T be the first time $X$ hits $(1,0)$ (which is a.s. finite). Is there any known bound on $\mathbb{P}(T>t)$, for $t$ large? I would like basically to know if it decays as a power or $t$, or more slowly.