The problem of recovering, say, a band-limited weakly stationary process from a set of its irregularly spaced samples is studied. For rather general sampling sequences some sufficient conditions ensuring mean square or pathwise reconstruction are obtained. For the cases of regular samples with either finitely many missing ones and/or finitely many irregular ones, a necessary and sufficient condition is presented. Some elements of the proofs involve classical results on nonharmonic Fourier series as well as more recent results on frames.
"Reconstruction of Band Limited Processes from Irregular Samples." Ann. Probab. 23 (2) 674 - 696, April, 1995. https://doi.org/10.1214/aop/1176988284