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Smoothness properties of the conditional expectation in finitely additive white noise filtering

Author

Listed:
  • Hucke, H. P.
  • Kallianpur, G.
  • Karandikar, R. L.

Abstract

It is shown that for a wide class of signal processes and bounded g, the conditional expectation [pi](g, y) in the white noise filtering model is a C[infinity]-functional of the observations in the sense that [pi](g, y) and its Fréchet derivatives (which exist) are random variables on the quasicylindrical probability space on which the observation model is defined.

Suggested Citation

  • Hucke, H. P. & Kallianpur, G. & Karandikar, R. L., 1988. "Smoothness properties of the conditional expectation in finitely additive white noise filtering," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 261-269, October.
    • Handle: RePEc:eee:jmvana:v:27:y:1988:i:1:p:261-269
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