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.File allegati a questo prodotto
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