On a Characterization of Linear Stochastic Systems and its Applications

Abstract

By regarding random variables as vectors in a Hilbert space an interesting characterization of a stochastic system has been developed. Some of the issues like designing a digital filter using second order statistics [6], the predictor space representation for Autoregressive Moving Average (ARMA) processes [5] and minimal realization of a non-stochastic system [2], are re-examined in this light.

Indexing terms:

• Linear stochastic systems
• Autoregressive moving average process
• Digital filter
• Decoupled system identification
• Minimal realization algorithm