Journal of Applied Probability

Generalized telegraph process with random jumps

Antonio Di Crescenzo, Antonella Iuliano, Barbara Martinucci, and Shelemyahu Zacks

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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.

Article information

J. Appl. Probab., Volume 50, Number 2 (2013), 450-463.

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60J75: Jump processes

Jump-telegraph process alternating renewal process exponential random time random jump


Di Crescenzo, Antonio; Iuliano, Antonella; Martinucci, Barbara; Zacks, Shelemyahu. Generalized telegraph process with random jumps. J. Appl. Probab. 50 (2013), no. 2, 450--463. doi:10.1239/jap/1371648953.

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