Integrated fractional Brownian motion: persistence probabilities and their estimates

Abstract: The problem is a log-asymptotics of the probability that the Integrated fractional Brownian motion of index 0<H<1 does not exceed a fixed level during long time. For the growing time interval (0,T) the hypothetical log-asymptotics is (H(H-1)+o(1))Log T. In support of the hypothesis, we update our earlier estimates of the probability and give analytical proofs.