  In this paper, we study the recovery of the Hurst parameter from a given
discrete sample of fractional Brownian motion with statistical inverse theory.
In particular, we show that in the limit the posteriori distribution of the
parameter given the sample determines the parameter uniquely. In order to
obtain this result, we first prove various strong laws of large numbers related
to the problem at hand and then employ these limit theorems to verify directly
the limiting behaviour of posteriori distributions without making additional
technical or simplifying assumptions that are commonly used.
