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On the Asymmetric Telegraph Processes

Part of: Special processes Limit theorems Markov processes

Published online by Cambridge University Press:  19 February 2016

Oscar López  and
Nikita Ratanov
Oscar López*
Affiliation:
Universidad del Rosario
*
∗ Postal address: Universidad del Rosario, Cl. 12c, No. 4-69, Bogotá, Colombia.
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Abstract

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We study the one-dimensional random motion X = X(t), t ≥ 0, which takes two different velocities with two different alternating intensities. The closed-form formulae for the density functions of X and for the moments of any order, as well as the distributions of the first passage times, are obtained. The limit behaviour of the moments is analysed under nonstandard Kac's scaling.

Keywords

Asymmetric telegraph processfirst passage timeKac's asymptoticsmomentsmodified Bessel functionKummer function

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J65: Brownian motion 60F05: Central limit and other weak theorems 60K99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 569 - 589
Copyright
© Applied Probability Trust 

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