Journal of Applied Probability

Generalized telegraph process with random jumps

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

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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.

Article information

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

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648953

Digital Object Identifier
doi:10.1239/jap/1371648953

Mathematical Reviews number (MathSciNet)
MR3102492

Zentralblatt MATH identifier
1277.60147

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

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

Citation

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. https://projecteuclid.org/euclid.jap/1371648953


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