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Detailed probabilistic analysis of the integrated three-valued telegraph signal

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Ilaria Di Matteo  and
Enzo Orsingher
Ilaria Di Matteo*
Affiliation:
University of Rome ‘La Sapienza'
Enzo Orsingher*
Affiliation:
University of Rome ‘La Sapienza'
*
∗Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome ‘La Sapienza', Piazzale Aldo Moro 5, 00185 Rome, Italy.
∗Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome ‘La Sapienza', Piazzale Aldo Moro 5, 00185 Rome, Italy.
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Abstract

In this paper the integrated three-valued telegraph process is examined. In particular, the third-order equations governing the distributions , (where N(t) denotes the number of changes of the telegraph process up to time t) are derived and recurrence relationships for them are obtained by solving suitable initial-value problems. These recurrence formulas are related to the Fourier transform of the conditional distributions and are used to obtain explicit results for small values of k. The conditional mean values (where V(0) denotes the initial velocity of motions) are obtained and discussed.

Keywords

HYPERBOLIC EQUATIONSPOISSON PROCESSINITIAL-VALUE PROBLEMSFOURIER TRANSFORMSFORCED WAVE EQUATION

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 671 - 684
Copyright
Copyright © Applied Probability Trust 1997 

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References

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