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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