ANALYSIS OF THE STOCHASTIC FITZHUGH–NAGUMO SYSTEM

Stefano Bonaccorsi, Elisa Mastrogiacomo

Type: Article

Publication Date: 2008-09-01

Citations: 29

DOI: https://doi.org/10.1142/s0219025708003191

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 mainly be 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).

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Works Cited by This (7)

Action	Title	Year	Authors
+	Ergodicity for Infinite Dimensional Systems	1996	Giuseppe Da Prato Jerzy Zabczyk
+	Second Order Partial Differential Equations in Hilbert Spaces	2002	Giuseppe Da Prato Jerzy Zabczyk
+	Equazioni differenziali nel campo reale	1948	Giovanni Sansone
+	Towards a ?matrix theory? for unbounded operator matrices	1989	Rainer Nagel
+	Kolmogorov Equations for Stochastic PDEs	2004	Giuseppe Da Prato
+	ERGODICITY FOR INFINITE DIMENSIONAL SYSTEMS (London Mathematical Society Lecture Note Series 229)	1997	K. D. Elworthy
+	Stochastic Equations in Infinite Dimensions	1992	Guiseppe Da Prato Jerzy Zabczyk