Abstract
Our focus is related to the problem of small perturbations. For the sake of illustration, we first consider the dynamical system in series scheme
where y(t) is a certain stochastic process, ε>0is a small parameter and g is a given function. If function g does not increase too fast, then the solution of Z ε t converges to Z 0 t ≡ z as ε→0, uniformly on every finite time interval [0,T]. However, the behavior of Z ε t on time intervals of order ε-1 or of higher orders (for example,ε-2) is usually of great interest and, on these intervals significant changes occur.
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© 2003 Springer Science+Business Media Dordrecht
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Swishchuk, A., Wu, J. (2003). Limit Theorems For Difference Equations in Random Media. In: Evolution of Biological Systems in Random Media: Limit Theorems and Stability. Mathematical Modelling: Theory and Applications, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1506-5_2
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DOI: https://doi.org/10.1007/978-94-017-1506-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6398-4
Online ISBN: 978-94-017-1506-5
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