On a very tight truncation error bound for stationary stochastic processes

A very tight truncation error upper bound is established for bandlimited weakly stationary stochastic processes if the sampling interval is closed. In particular, the magnitude of the upper bound is O(N^-2q ln² N) for a symmetric sampling reconstruction from 2N+1 sampled values, where q is an arbitrary positive integer. The results are derived with the help of the Bernstein bound on the remainder of a symmetric complex Fourier series of the function exp (iλ t). Convergence rates are given for mean square and almost sure sampling reconstructions