400 research outputs found
Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions
We prove local existence of solutions for a class of suitably renormalised
coupled SPDE-ODE systems driven by space-time white noise, where the space
dimension is equal to 2 or 3. This class includes in particular the
FitzHugh-Nagumo system describing the evolution of action potentials of a large
population of neurons, as well as models with multidimensional gating
variables. The proof relies on the theory of regularity structures recently
developed by M. Hairer, which is extended to include situations with semigroups
that are not regularising in space. We also provide explicit expressions for
the renormalisation constants, for a large class of cubic nonlinearities.Comment: 51 pages. The extension procedure in Section 4 has been substantially
modified. Minor changes in Sections 5 and 6 and in the main resul
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