Periodic sampling of random processes can be altered by several phenomena. Jitter is a one of them, which was studied for a long time. This paper investigates the problem of a random integration width in the periodic sampling process. Taking into account the statistics of the random integration width, the expression of the best linear reconstruction (in the mean square sense) of the continuous process is given, based on the observation of the samples. Particular examples are given with a comparison with the Shannon interpolator.