From persistent random walks to the telegraph noise

Details From persistent random walks to the telegraph noise From persistent random walks to the telegraph noise

2008-10-03

arxiv.org/abs/0810.0650v1

Mathematics

Probability

Scientific paper

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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