From persistent random walks to the telegraph noise

Samuel Herrmann; Pierre Vallois

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arXiv · 0810.0650

From persistent random walks to the telegraph noise

Samuel Herrmann·Pierre Vallois

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Abstract

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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BibTeX RIS

Samuel Herrmann, Pierre Vallois. 2008-10-03. From persistent random walks to the telegraph noise. https://arxiv.org/abs/0810.0650

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