Characterizing attraction probabilities via the stochastic Zubov equation

L. Grüne, F. Camilli: Characterizing attraction probabilities via the stochastic Zubov equation
Discrete and Continuous Dynamical Systems - Series B 3, 457 - 468, 2003

DOI: 10.3934/dcdsb.2003.3.457
Keywords: stochastic differential equation; almost sure exponential stability; Zubov's method; viscosity solution
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Abstract:

A stochastic differential equation with an a.s. locally stable fixed point is considered. The attraction probabilities to the fixed point are characterized by the sublevel sets of the limit of a sequence of solutions to 2nd order partial differential equations. A numerical example to illustrate the method is presented.

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