A Consistent Estimate of the Deterministic Dead Time from Observations of the MAP Flow

In this paper, recurrent MAP flows are constructed using a Markov?modulated Poisson process. Given the deterministic dead time for these flows, recurrent observation flows are determined. Dead times are estimated as the minimum distances between adjacent observation times. The validity of these estimates is proved using an upper bound for the jump size of the random walk defined by the recurrent MAP flow. This upper bound is investigated using the continuity theorem for uniformly convergent series of continuous functions and the Weierstrass theorem on the maximum of a continuous function on a segment.