# American Institute of Mathematical Sciences

August  2003, 3(3): 457-468. doi: 10.3934/dcdsb.2003.3.457

## Characterizing attraction probabilities via the stochastic Zubov equation

 1 Sez. di Matematica per I'Ingegneria, Dip. di Matematica Pura e Applicata, Università dell'Aquila, 67040 Roio Poggio (AQ), Italy 2 Mathematisches Institute, Universität Bayreuth, 95440 Bayreuth, Germany

Received  November 2002 Revised  February 2003 Published  May 2003

A stochastic differential equation with an a.s. locally stable compact set is considered. The attraction probabilities to the set are characterized by the sublevel sets of the limit of a sequence of solutions to $2^{nd}$ order partial differential equations. Two numerical examples illustrating the method are presented.
Citation: Fabio Camilli, Lars Grüne. Characterizing attraction probabilities via the stochastic Zubov equation. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 457-468. doi: 10.3934/dcdsb.2003.3.457
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