Poincaré type inequalities for compact degenerate pure jump Markov processes

Abstract

We aim in proving Poincaré inequalities for a class of pure jump Markov processes inspired by the model introduced in \cite{G-L} by Galves and Löcherbach to describe the behaviour of interacting brain neurons. In particular, we consider neurons with degenerate jumps, i.e. that lose their memory when they spike, while the probability of a spike depends on the actual position and thus the past of the whole neural system.

References in corpus (5)

• Lasso and probabilistic inequalities for multivariate point processes
• Entropies, convexity, and functional inequalities
• Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets
• A model for neural activity in the absence of external stimuli
• Fluid limit theorems for stochastic hybrid systems with application to neuron models

Cited by in corpus (2)

• Modified log-Sobolev inequality for a compact PJMP with degenerate jumps
• Concentration and Poincaré type inequalities for a degenerate pure jump Markov process