How long does a clock error remain inside two threshold barriers? An evaluation by means of stochastic processes

In this paper we study the atomic clock error by using the stochastic differential equations. In particular, we focus on the evaluation of the "survival probability", that is the probability that clock error exceeds the limit of permissible error at a certain time after synchronization. The results are applied to experimental cases where the typical noise parameters of atomic clocks are considered. We also determine the optimal calibration intervals of measuring instruments as GNSS clock making use of the discussed results.