An upper bound on the mean-square error in the sampling expansion for non-band-limited processes

An upper bound is obtained on the mean-square error involved when a real-valued non-band-limited nonstationary random process x(t) is approximated by the sampling expansion

$\text{∑}\text{n=?∞}\text{∞}\text{x(nT)}\text{sin}\text{π(t?nT)/T}\text{π(t?nT)/T}$

for some T > 0. When the process x(t) is band-limited over $\text{?}\text{1}\text{2T}\text{,}\text{1}\text{2T}$], this error bound reduces to zero.