Bjoernsson, Hjortur, Hafstein, Sigurdur, Giesl, Peter, Scalas, Enrico and Gudmundsson, Skuli (2019) Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function. Discrete and Continuous Dynamical Systems - Series B, 24 (8). pp. 4247-4269. ISSN 1531-3492

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Abstract

The y-basin of attraction of the zero solution of a nonlinear stochastic differential equation can be determined through a pair of a local and a non-local Lyapunov function. In this paper, we construct a non-local Lyapunov function by solving a second-order PDE using meshless collocation. We provide a-posteriori error estimates which guarantee that the constructed function is indeed a non-local Lyapunov function. Combining this method with the computation of a local Lyapunov function for the linearisation around an equilibrium of the stochastic differential equation in question, a problem which is much more manageable than computing a Lyapunov function in a large area containing the equilibrium, we provide a rigorous estimate of the stochastic y-basin of attraction of the equilibrium.

Item Type:	Article
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups:	Analysis and Partial Differential Equations Research Group Probability and Statistics Research Group
Subjects:	Q Science > QA Mathematics
Depositing User:	Alice Jackson
Date Deposited:	07 Nov 2018 15:56
Last Modified:	01 Apr 2020 01:00
URI:	http://sro.sussex.ac.uk/id/eprint/80036

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