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, Stefano
Primo
;
Mastrogiacomo, Elisa
Ultimo
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).
2008
Trento
Università degli Studi di Trento, Dipartimento di Matematica
Analysis of the stochastic FitzHugh-Nagumo system / Bonaccorsi, Stefano; Mastrogiacomo, Elisa. - ELETTRONICO. - (2008), pp. 1-20.
Bonaccorsi, Stefano; Mastrogiacomo, Elisa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/359328
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