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Article Dans Une Revue Stochastics and Dynamics Année : 2010

From persistent random walks to the telegraph noise

Résumé

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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Dates et versions

hal-00326521 , version 1 (03-10-2008)

Identifiants

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Samuel Herrmann, Pierre Vallois. From persistent random walks to the telegraph noise. Stochastics and Dynamics, 2010, 10 (2), pp.161-196. ⟨10.1142/S0219493710002905⟩. ⟨hal-00326521⟩
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