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1 results

  • A uniqueness problem for the envelope of an oscillatory process

  • A. M. Hasofer
  • Journal:
    Journal of Applied Probability / Volume 16 / Issue 4 / December 1979
    Published online by Cambridge University Press:
    14 July 2016, pp. 822-829
    Print publication:
    December 1979

  • In a previous paper, the author has described a method for obtaining envelope processes for oscillatory stochastic processes. These are processes which can be represented as the output of a time-varying linear filter whose input is a stationary process.

    It is shown in this paper that the proposed definition of the envelope process may not be unique, but may depend on the particular representation of the oscillatory process chosen.

    It is then shown that for a class of oscillatory processes which is of particular interest, the class of transient processes, there is a class of natural representations which all lead to a unique envelope process.