On the Dispersion of Time-Dependent Means of a Stationary Stochastic Process

Let $\xi(t)$ be a stationary process in the wide sense with discrete (continuous) time $\xi(t)=0$
$$\zeta_p=\sum\limits_{t=0}^{p-1}{\xi(t)}\,\left({\zeta_p=\int_0^p{\xi(t)\,dt}}\right),\\ b_p=\mathbf M|{\xi_p} |^2.$$
The behaviour of $b_p$ for $p\to\infty$ is dealt with in the paper.