scholarly journals Spatial ergodicity for SPDEs via Poincaré-type inequalities

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Le Chen ◽  
Davar Khoshnevisan ◽  
David Nualart ◽  
Fei Pu
Keyword(s):  
Poincaré Type Inequalities

New Poincaré-type inequalities

2014 ◽  
Vol 352 (2) ◽  
pp. 163-166 ◽  
Author(s):  
Sebastian Bauer ◽  
Patrizio Neff ◽  
Dirk Pauly ◽  
Gerhard Starke
Keyword(s):  
Poincaré Type Inequalities

scholarly journals Poincaré-Type Inequalities for Compact Degenerate Pure Jump Markov Processes

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 518 ◽  
Author(s):  
Pierre Hodara ◽  
Ioannis Papageorgiou
Keyword(s):  
Membrane Potential ◽  
Point Process ◽  
Markov Processes ◽  
Relevant Information ◽  
Neural System ◽  
Brain Neurons ◽  
Actual Position ◽  
The Past ◽  
Poincaré Type Inequalities ◽  
Jump Markov Processes

We aim to prove Poincaré inequalities for a class of pure jump Markov processes inspired by the model introduced by Galves and Löcherbach 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 Löcherbach 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.

Hardy-Poincaré Type Inequalities Related to k-Hessian Operator

2020 ◽  
Vol 14 (8) ◽  
Author(s):  
Yongyang Jin ◽  
Haiting Chen ◽  
Shoufeng Shen ◽  
Yurong Wu
Keyword(s):  
Hessian Operator ◽  
Poincaré Type Inequalities
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