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June 2013 Generalized telegraph process with random jumps
Antonio Di Crescenzo, Antonella Iuliano, Barbara Martinucci, Shelemyahu Zacks
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J. Appl. Probab. 50(2): 450-463 (June 2013). DOI: 10.1239/jap/1371648953

Abstract

We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at time t=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.

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Antonio Di Crescenzo. Antonella Iuliano. Barbara Martinucci. Shelemyahu Zacks. "Generalized telegraph process with random jumps." J. Appl. Probab. 50 (2) 450 - 463, June 2013. https://doi.org/10.1239/jap/1371648953

Information

Published: June 2013
First available in Project Euclid: 19 June 2013

zbMATH: 1277.60147
MathSciNet: MR3102492
Digital Object Identifier: 10.1239/jap/1371648953

Subjects:
Primary: 60K15
Secondary: 60J75

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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