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Stochastic neural field equations: A rigorous footing

Olivier Faugeras 1 James Inglis 1, 2 
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We here consider a stochastic version of the classical neural field equation that is currently actively studied in the mathematical neuroscience community. Our goal is to present a well-known rigorous probabilistic framework in which to study these equations in a way that is accessible to practitioners currently working in the area, and thus to bridge some of the cultural/scientific gaps between probability theory and mathematical biology. In this way, the paper is intended to act as a reference that collects together relevant rigorous results about notions of solutions and well-posedness, which although may be straightforward to experts from SPDEs, are largely unknown in the neuroscientific community, and difficult to find in a very large body of literature. Moreover, in the course of our study we provide some new specific conditions on the parameters appearing in the equation (in particular on the neural field kernel) that guarantee the existence of a solution.
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Submitted on : Tuesday, December 16, 2014 - 3:51:48 PM
Last modification on : Thursday, August 4, 2022 - 4:58:17 PM
Long-term archiving on: : Monday, March 23, 2015 - 2:16:26 PM


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  • HAL Id : hal-00907555, version 2
  • ARXIV : 1311.5446


Olivier Faugeras, James Inglis. Stochastic neural field equations: A rigorous footing. Journal of Mathematical Biology, 2014, pp.40. ⟨hal-00907555v2⟩



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