Telegraph processes with random velocities

Autor(en): Stadje, W 
Zacks, S
Stichwörter: exact distribution; hitting time; integro-differential equation; Mathematics; MAXIMUM DISPLACEMENT; RANDOM MOTIONS; random velocity; Statistics & Probability; telegraph process; TIMES
Erscheinungsdatum: 2004
Herausgeber: CAMBRIDGE UNIV PRESS
Journal: JOURNAL OF APPLIED PROBABILITY
Volumen: 41
Ausgabe: 3
Startseite: 665
Seitenende: 678
Zusammenfassung: 
We study a one-dimensional telegraph process (M-t)(tgreater than or equal to0) 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.
ISSN: 00219002
DOI: 10.1239/jap/1091543417

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