On time-reversibility of linear stochastic models

Abstract: Reversal of the time direction in stochastic systems driven by white noise has been central throughout the development of stochastic realization theory, filtering and smoothing. Similar ideas were developed in connection with certain problems in the theory of moments, where a duality induced by time reversal was introduced to parametrize solutions. In this latter work it was shown that stochastic systems driven by arbitrary second-order stationary processes can be similarly time-reversed. By combining these two sets of ideas we present herein a generalization of time-reversal in stochastic realization theory.