Limit Theorems for Certain Functionals of Unions of Random Closed Sets

For the fractional Brownian motion (fBm) the problem of extrapolation from a segment, the canonical representation of fBm via white noise on a segment and their reciprocal relation, and Girsanovʹs formula are considered. A general approach to these problems is based on the invariance of fBm with respect to linear rational transformations of time. This approach practically excludes the solution of integral equations and explains the efficiency of the aforementioned problems for~fBm.