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Article Dans Une Revue Journal of Mathematical Biology Année : 2014

Stochastic neural field equations: A rigorous footing

Résumé

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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Dates et versions

hal-00907555 , version 1 (21-11-2013)
hal-00907555 , version 2 (16-12-2014)

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Citer

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