Poincare-Type Inequalities for Compact Degenerate Pure Jump Markov Processes

Autor(es)

Hodara, Pierre ^[1] ; Papageorgiou, Ioannis ^[2]

Afiliação do(s) autor(es)

^[1] INRA, MaIAGE, Allee Vilvert, F-78352 Jouy En Josas - France

^[2] Univ Sao Paulo, Inst Matemat & Estat, Neuromat, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICS; v. 7, n. 6 JUN 2019.
• Citações Web of Science: 1

Resumo

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. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Oswaldo Baffa Filho
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 17/15587-8 - Dinâmicas estocásticas de redes neurais
• Beneficiário: Ioannis Papageorgiou
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 16/17655-8 - Modelização e estimação de redes neurais
• Beneficiário: Pierre Hodara
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado