We study a one-dimensional telegraph process ( M t ) t ≥0 describing the position of a particle moving at constant speed between Poisson times at which new velocities are chosen randomly. The exact distribution of M t and its first two moments are derived. We characterize the level hitting times of M t in terms of integro-differential equations which can be solved in special cases.
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Stadje et al. (2004) studied this question.
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