  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.
