Random perturbations of recursive sequences with an application to an epidemic model
- 1 September 1995
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 32 (3) , 559-578
- https://doi.org/10.2307/3215113
Abstract
We investigate the asymptotic sample path behaviour of a randomly perturbed discrete-time dynamical system. We consider the case where the trajectories of the non-perturbed dynamical system are attracted by a finite number of limit sets and characterize a case where this property remains valid for the perturbed dynamical system when the perturbation converges to zero. For this purpose, no further assumptions on the perturbation are needed and our main condition applies to the limit sets of the non-perturbed dynamical system. When the limit sets reduce to limit points we show that this main condition is more general than the usual assumption of the existence of a Lyapunov function for the non-perturbed dynamical system. An application to an epidemic model is given to illustrate our results.Keywords
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