A talk on topics of finance, insurance, and mathematics:
"From persistent random walk to the telegraph noise"
Pierre Vallois, Professor at the Universite de Nancy I
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 easily 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 >= 0).