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A unique representation theorem for the conditional expectation of stationary processes and application to dynamic estimation problems
Part of
- Stochastic processes
- Nonparametric inference
Marco Campi
Journal:

Journal of Applied Probability / Volume 34 / Issue 2 / June 1997

Published online by Cambridge University Press:

14 July 2016, pp. 372-380

Print publication:

June 1997
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In this paper, multivariate strict sense stationary stochastic processes are considered. It is shown that there exists a universal function by means of which the conditional expectation of any stationary process with respect to its past can be represented. This requires no ergodicity assumptions. The important implications of this result in the evaluation of the achievable performance in certain dynamic estimation problems with incomplete statistical information are also discussed.

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A unique representation theorem for the conditional expectation of stationary processes and application to dynamic estimation problems