ISSN:
1572-9222
Keywords:
Difference equations
;
random perturbation
;
averaging
;
diffusion approximation
;
randomly perturbed iterations
;
stability
;
3SR60
;
60H15
;
60J99
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02227491
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