Asymptotic Behavior of the Linear Prognosis Error for a Class of Stochastic Processes

Estimates are obtained for the quantities $\delta_T(\tau)=\sigma^2_T(\tau)-\sigma^2(\tau)$ and $J(\xi^\infty_0,\xi^{-T}_{-\infty}/\xi^0_{-T}$ [where $\sigma^2_T(\tau)$ is the error of prognosis from an earlier $T$ to a future $\tau$] for a certain class of stochastic processes. It turns out that these quantities decay according to a power law.