Distributions and Direct Parametrization for Stable Stochastic State-Space Models

We present a direct parametrization for continuous-time stochastic state-space models that ensures external stability via the stochastic bounded-real lemma. Our formulation facilitates the construction of probabilistic priors that enforce almost-sure stability, which are suitable for sampling-based Bayesian inference methods. We validate our work with a simulation example and demonstrate its ability to yield stable predictions with uncertainty quantification.