Characterizing attraction probabilities via the stochastic Zubov equation

Fabio Camilli; Lars Grüne

doi:10.3934/dcdsb.2003.3.457

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2003, Volume 3, Issue 3: 457-468. Doi: 10.3934/dcdsb.2003.3.457

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Characterizing attraction probabilities via the stochastic Zubov equation

Fabio Camilli^1, and
Lars Grüne^2,

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

Received: November 2002

Revised: February 2003

Published: August 2003

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 60H10, 93E15, 49L25.

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