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Published online by Cambridge University Press: 22 January 2016
Let Xt be a stochastic process and Yt be its square process. The present note is concerned with the solution of the equation assuming Yt is given. In [4], F. A. Grünbaum proved that certain statistics of Yt are enough to determine those of Xt when it is a centered, nonvanishing, Gaussian process with continuous correlation function. In connection with this result, we are interested in sample function-wise inference, though it is far from generalities. A glance of the equation shows that the difficulty is related how to pick up a sign of . Thus if we know that Xt has nice sample process such as the zero crossings are finite, no tangencies, in any finite time interval, then observations of these statistics will make it sure to find out sample functions of Xt from those of Yt (see [2]). The purpose of this note is to consider the above problem from this point of view.