# On stochastic stabilization of difference equations

@article{Appleby2006OnSS,
title={On stochastic stabilization of difference equations},
author={John A. D. Appleby and Xuerong Mao and Alexandra Rodkina},
journal={Discrete and Continuous Dynamical Systems},
year={2006},
volume={15},
pages={843-857}
}
• Published 1 April 2006
• Mathematics
• Discrete and Continuous Dynamical Systems
We consider unstable scalar deterministic difference equation $x_{n+1}=x_n(1+a_nf(x_n))$, $n\ge 1$, $x_0=a$. We show how this equation can be stabilized by adding the random noise term $\sigma_ng(x_n)\xi_{n+1}$ where $\xi_n$ takes the values +1 or -1 each with probability $1/2$. We also prove a theorem on the almost sure asymptotic stability of the solution of a scalar nonlinear stochastic difference equation with bounded coefficients, and show the connection between the noise…
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