Concentration and Poincar\'e type inequalities for a degenerate pure jump Markov process

Pierre Hodara; Ioannis Papageorgiou

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arXiv · 1904.07090

Concentration and Poincar\'e type inequalities for a degenerate pure jump Markov process

Pierre Hodara·Ioannis Papageorgiou

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Abstract

We study Talagrand concentration and Poincar\'e 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 L\"ocherbach in \cite{G-L}, in order to describe the activity of a biological neural network. As a result we obtain exponential rates of convergence to equilibrium.

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Pierre Hodara, Ioannis Papageorgiou. 2019-04-12. Concentration and Poincar\'e type inequalities for a degenerate pure jump Markov process. https://arxiv.org/abs/1904.07090

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