On Multiple-Valued Random Functions
J. L. Lumley · Journal of Mathematical Physics · 1964
A technique is developed for the statistical description of multiple-valued functions. For the special case of single-valued functions, the relations developed are shown to reduce in a natural way to the customary ones. Transformation laws are developed relating the statistical descriptions of a multiple-valued function in two coordinate systems. The relationship of the present work to the Rice formula for the zeros of a random function is shown. The statistical description of homogeneous, isotropic, multiple-valued functions in two dimensions is developed. Previously known results regarding expected arc length of random functions are obtained using the present technique.