From persistent random walks to the telegraph noise

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We study a family of memory-based persistent random walks and we prove weak convergences after space-time rescaling. The limit processes are not only Brownian motions with drift. We have obtained a continuous but non-Markov process $(Z_t)$ which can be easely expressed in terms of a counting process $(N_t)$. In a particular case the counting process is a Poisson process, and $(Z_t)$ permits to represent the solution of the telegraph equation. We study in detail the Markov process $((Z_t,N_t); t\ge 0)$.

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Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/170652

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0810.0650
 http://arxiv.org/abs/0810.0650

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arXiv