Some new stochastic stability robustness bounds for state space models are reported in this work. Nominally exponentially stable discrete time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness. The methods employed in the analysis are the existing ones used in the deterministic framework by transforming the stochastic robustness problem to a deterministic one. The results are compared with each other and with the exact stability region in an example.