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Telegraph processes with random velocities

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

W. Stadje  and
S. Zacks
W. Stadje*
Affiliation:
University of Osnabrück
S. Zacks*
Affiliation:
Binghamton University
*
∗ Postal address: Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany. Email address: wolfgang@mathematik.uni-osnabrueck.de
∗∗ Postal address: Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA
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Abstract

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.

Keywords

Telegraph processrandom velocityhitting timeexact distributionintegro-differential equation

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60K15: Markov renewal processes, semi-Markov processes 60K40: Other physical applications of random processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 665 - 678
Copyright
Copyright © Applied Probability Trust 2004 

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