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Generalized integrated telegraph processes and the distribution of related stopping times

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

S. Zacks
S. Zacks*
Affiliation:
Binghamton University
*
∗ Postal address: Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA. Email address: [email protected]
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Abstract

Let {X(t), V(t), t ≥ 0} be a telegraph process, with V(0+) = 1. The distribution of X(t) is derived for the general case of an alternating renewal process, describing the length of time a particle is moving to the right or to the left. The distributions of the first-crossing times of given levels a and −a are studied for M/G and for G/M processes.

Keywords

Telegraph processalternating renewal processcompound Poissonupper and lower crossing times

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 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 2 , June 2004 , pp. 497 - 507
Copyright
Copyright © Applied Probability Trust 2004 

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