Analysis of the stochastic FitzHugh-Nagumo system

Bonaccorsi, Stefano and Mastrogiacomo, Elisa (2008) Analysis of the stochastic FitzHugh-Nagumo system. UNSPECIFIED. (Unpublished)

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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 Pt; further, we identify its infinitesimal generator in the space L2(H ; ν).

    Item Type: Departmental Technical Report
    Department or Research center: Mathematics
    Subjects: UNSPECIFIED
    Uncontrolled Keywords: Stochastic FitzHugh-Nagumo system; Invariant measures; Wiener process; Transition semigroup; Kolmogorov operator 1991 MSC: 35K57; 60H15; 37L40
    Report Number: UTM 719, January 2008
    Repository staff approval on: 25 Feb 2008

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