  The Shannon sampling theorem for bandlimited wide sense stationary random
processes was established in 1957, which and its extensions to various random
processes have been widely studied since then. However, truncation of the
Shannon series suffers the drawback of slow convergence. Specifically, it is
well-known that the mean-square approximation error of the truncated series at
$n$ points sampled at the exact Nyquist rate is of the order
$O(\frac1{\sqrt{n}})$. We consider the reconstruction of bandlimited random
processes from finite oversampling points, namely, the distance between
consecutive points is less than the Nyquist sampling rate. The optimal
deterministic linear reconstruction method and the associated intrinsic
approximation error are studied. It is found that one can achieve
exponentially-decaying (but not faster) approximation errors from oversampling.
Two practical reconstruction methods with exponential approximation ability are
also presented.
