Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise

@article{Appleby2009NonexponentialSA,
  title={Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise},
  author={John A. D. Appleby and Gregory Berkolaiko and Alexandra Rodkina},
  journal={Stochastics},
  year={2009},
  volume={81},
  pages={127 - 99}
}
We consider the stochastic difference equation where f and g are nonlinear, bounded functions, is a sequence of independent random variables, and h>0 is a nonrandom parameter. We establish results on asymptotic stability and instability of the trivial solution . We also show that, for some natural choices of f and g, the rate of decay of is approximately polynomial: there exists such that decays faster than but slower than , for any . It turns out that, if decays faster than as , the polynomial… 
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