Abstract
In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation.We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process.Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
15 articles.
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1. References;Asymptotic and Analytic Methods in Stochastic Evolutionary Systems;2023-08-04
2. Time to reach the maximum for a stationary stochastic process;Physical Review E;2022-11-03
3. Generalized Telegraph Process with Random Delays;Journal of Applied Probability;2012-09
4. Generalized Telegraph Process with Random Delays;Journal of Applied Probability;2012-09
5. On the Generalized Telegraph Process with Deterministic Jumps;Methodology and Computing in Applied Probability;2011-06-19