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1 results

  • A note on Gaussian processes and zero-memory non-linear transformations

  • Elias Masry
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 4 / December 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 857-861
    Print publication:
    December 1977

  • We consider the problem of the distinguishability between Gaussian processes observed through non-linear systems. For a broad class 𝒜 of zero-memory time-dependent non-linear transformations, the following uniqueness relationship is obtained. If Xi, i = 1, 2 are two normalized jointly Gaussian processes, then they are indistinguishable if and only if their transformed processes Yi = A[Xi], i = 1, 2, A ∈ 𝒜, are indistinguishable. Some interesting examples of functions in 𝒜 are presented.