Grain Boundary Triple Junction Effects on the Fatigue Deformation and Cracking Behaviors of Copper Tricrystal and Tetracrystals

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.