# 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} }

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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