Analysis of the stochastic FitzHugh-Nagumo system

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In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be mainly concerned with the asymptotic behaviour of the solution. We prove the existence of an invariant ergodic measure $ν$ associated with the transition semigroup $P_t$; further, we identify its infinitesimal generator in the space $L^2(H;ν)$.
20 pages

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Probability, Analysis of PDEs, 35K57; 60H15; 37L40

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http://salesiana.dossiersoluciones.com/handle/123456789/145993

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.2325
 http://arxiv.org/abs/0801.2325

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arXiv