Appleby, John A. D; Mao, Xuerong; Rodkina, Alexandra
Author Affiliation, Ana.
On stochastic stabilization of difference equations
Discrete and Continuous Dynamical Systems
Date of Publication
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.....