- Existence and stability of stationary solutions of nonlinear difference equations under random perturbations
- Journal of Difference Equations and Applications
- Volume | Issue number
- 17 | 4
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
Existence and stability of stationary solutions of nonlinear random difference equations are studied in this note. Firstly, we give the weak conditions that guarantee the continuity of Lypanunov exponents under small random perturbations. Secondly, we find out the conditions under which the ratio of the random norm and the standard Euclidean norm has deterministic bounds. Based on these new results, we provide easy-to-use conditions that guarantee the existence and almost sure stability of a stationary solution. In addition, we also prove that the stationary solution converges with probability one to the fixed point of the corresponding deterministic system as the noise intensity tends to zero.
- go to publisher's site
- This is an Author's Accepted Manuscript of an article published in: Mei Zhu, Duo Wang & Maozheng Guo (2011): Existence and stability of stationary solutions of nonlinear difference equations under random perturbations, Journal of Difference Equations and Applications, 17:04, 587-602. Version of record first published: 08 Sep 2010, copyright Taylor & Francis, available online at: http://dx.doi.org/10.1080/10236190903257826.
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.