  We construct the least-square estimator for the unknown drift parameter in
the multifractional Ornstein-Uhlenbeck model and establish its strong
consistency in the non-ergodic case. The proofs are based on the asymptotic
bounds with probability 1 for the rate of the growth of the trajectories of
multifractional Brownian motion (mBm) and of some other functionals of mBm,
including increments and fractional derivatives. As the auxiliary results
having independent interest, we produce the asymptotic bounds with probability
1 for the rate of the growth of the trajectories of the general Gaussian
process and some functionals of it, in terms of the covariance function of its
increments.

Probability