Concentration and Poincaré type inequalities for a degenerate pure jump Markov process

Abstract

We study Talagrand concentration and Poincaré type inequalities for unbounded pure jump Markov processes. In particular we focus on processes with degenerate jumps that depend on the past of the whole system, based on the model introduced by Galves and Löcherbach, in order to describe the activity of a biological neural network. As a result we obtain concentration properties.