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Poincaré-Type Inequalities for Compact Degenerate Pure Jump Markov Processes

Abstract : We aim to prove Poincare inequalities for a class of pure jump Markov processes inspired by the model introduced by Galves and Locherbach to describe the behavior of interacting brain neurons. In particular, we consider neurons with degenerate jumps, i.e., which 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. The process studied by Galves and Locherbach is a point process counting the spike events of the system and is therefore non-Markovian. In this work, we consider a process describing the membrane potential of each neuron that contains the relevant information of the past. This allows us to work in a Markovian framework.
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https://hal.inrae.fr/hal-02877618
Déposant : Roselyne Tache <>
Soumis le : lundi 22 juin 2020 - 15:41:38
Dernière modification le : mardi 23 juin 2020 - 03:32:16

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Pierre Hodara, Ioannis Papageorgiou. Poincaré-Type Inequalities for Compact Degenerate Pure Jump Markov Processes. Mathematics , MDPI, 2019, 7 (6), pp.518. ⟨10.3390/math7060518⟩. ⟨hal-02877618⟩

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