We consider a stochastic differential equation with an asymptotically stable equilibrium point. We show that the domain of attraction of the equilibrium, i.e. the set of points which are attracted with positive probability to it, can be characterized by the solution of a suitable partial differential equation.

A Zubov's method for stochastic differential equations / Camilli, Fabio; Loreti, Paola. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 13:(2006), pp. 205-222. [10.1007/s00030-005-0036-1]

A Zubov's method for stochastic differential equations

CAMILLI, FABIO;LORETI, Paola
2006

Abstract

We consider a stochastic differential equation with an asymptotically stable equilibrium point. We show that the domain of attraction of the equilibrium, i.e. the set of points which are attracted with positive probability to it, can be characterized by the solution of a suitable partial differential equation.
Stochastic differential equation; almost sure exponential stability; Zubov’s method; viscosity solution
01 Pubblicazione su rivista::01a Articolo in rivista
A Zubov's method for stochastic differential equations / Camilli, Fabio; Loreti, Paola. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 13:(2006), pp. 205-222. [10.1007/s00030-005-0036-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/233909
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