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Noisy recurrent neural networks: the discrete-time case

The results of the companion paper on the behavior of continuous-time recurrent neural networks (RNN) are specialized to the discrete-time (so-called time-lagged recurrent) case. Uniform boundedness of the first and second moment sequences of the trajectory is established. For practical design purposes, estimates and bounds on the bias and variance sequences of the stochastic discrete-time RNN are derived. A script file for estimating the variance bounds for specified designs is provided in an Appendix.