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 Pt; further, we identify its infinitesimal generator in the space L2(H ; ν).
Analysis of the stochastic FitzHugh-Nagumo system / Bonaccorsi, Stefano; Mastrogiacomo, Elisa. - ELETTRONICO. - (2008), pp. 1-20.
Analysis of the stochastic FitzHugh-Nagumo system
Bonaccorsi, StefanoPrimo
;Mastrogiacomo, ElisaUltimo
2008-01-01
Abstract
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 Pt; further, we identify its infinitesimal generator in the space L2(H ; ν).File in questo prodotto:
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