  Available methods for identification of stochastic dynamical systems from
input-output data generally impose restricting structural assumptions on either
the noise structure in the data-generating system or the possible state
probability distributions. In this paper, we introduce a novel identification
method of such systems, which results in a dynamical model that is able to
produce the time-varying output distribution accurately without taking
restrictive assumptions on the data-generating process. The method is
formulated by first deriving a novel and exact representation of a wide class
of nonlinear stochastic systems in a so-called meta-state-space form, where the
meta-state can be interpreted as a parameter vector of a state probability
function space parameterization. As the resulting representation of the
meta-state dynamics is deterministic, we can capture the stochastic system
based on a deterministic model, which is highly attractive for identification.
The meta-state-space representation often involves unknown and heavily
nonlinear functions, hence, we propose an Artificial Neural Network (ANN)-based
identification method capable of efficiently learning nonlinear
meta-state-space models. We demonstrate that the proposed identification method
can obtain models with a log-likelihood close to the theoretical limit even for
highly nonlinear, highly stochastic systems.
