Analytical and Computational Problems Related to Fractional Gaussian Noise

We study the projection of an element fractional Gaussian noise onto its neighbouring elements. prove some analytic results for coefficients this projection. In particular, we obtain recurrence relations them. also make several conjectures concerning behaviour these coefficients, provide numerical evidence supporting conjectures, and them theoretically in particular cases. As auxiliary result independent interest, investigate covariance function noise, that it is completely monotone H>1/2, and, monotone, convex, log-convex along with further useful properties.