Deterministic Estimation and Asymptotic Stochastic Estimation

  • Omar Hijab
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 78)


Let t → x(t) be a state process and consider observations t → y(t) of a signal t → h(x(t)) in the presence of additive white noise ẏ = h(x) + v. The stochastic filter is the map that associates to each observation record y(τ), 0 ≤ τ ≤ t, the conditional mean E( ∅ (x(t)) ∣ y(τ), 0 ≤ τ ≤ t). In this paper it is shown that the output of the stochastic filter converges to the output of what is known as the deterministic filter as the variances of the impinging noises go to zero, exactly in analogy with the physical fact that quantum mechanics converges to classical mechanics as Plank’s constant goes to zero.


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  1. (1).
    Hijab,Omar, “Minimum Energy Estimation”, Ph.D. dissertation, University of California, Berkeley, December 1980.Google Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Omar Hijab
    • 1
  1. 1.Division of Applied SciencesPierce Hall Harvard UniversityCambridgeUSA

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