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Publication Type
Journal Article
UWI Author(s)
Author, Analytic
Appleby, John A. D; Mao, Xuerong; Rodkina, Alexandra
Author Affiliation, Ana.
n/a
Article Title
On stochastic stabilization of difference equations
Medium Designator
n/a
Connective Phrase
n/a
Journal Title
Discrete and Continuous Dynamical Systems
Translated Title
n/a
Reprint Status
Refereed
Date of Publication
2006
Volume ID
15
Issue ID
3
Page(s)
843-857
Language
n/a
Connective Phrase
n/a
Location/URL
.http:; www4.dcu.ie/maths/research/preprints/ms0513.pdf
ISSN
n/a
Notes
n/a
Abstract
We consider the unstable scalar deterministic difference equation xn+1 = xn_1 + anf(xn)_, n _ 1, x0 = a. It is shown how this equation can be stabilised by adding the noise term _ng(xn)_n+1 where _n takes the values 1 or -1, each with probability 1 2 . We also prove a theorem on the almost sure asymptotic stability of the solutions of scalar nonlinear stochastic difference equation with bounded coefficients, and show the connection between the noise stabilisation of stochastic differential equations, and discretisations of these equations.....
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