A UNIQUE REPRESENTATION THEOREM FOR THE CONDITIONAL-EXPECTATION OF STATIONARY-PROCESSES AND APPLICATION TO DYNAMIC ESTIMATION PROBLEMS

In this paper, multivariate strict sense stationary stochastic process es are considered. It is shown that there exists a universal function by means of which the conditional expectation of any stationary proces s with respect to its past can be represented. This requires no ergodi city assumptions. The important implications of this result in the eva luation of the achievable performance in certain dynamic estimation pr oblems with incomplete statistical information are also discussed.