On a class of processes arising in linear estimation theory

This paper considers a class of stochastic processes, called {em spherically invariant},which have the property that all mean-square estimation problems on them have linear solutions. It is shown that their multivariate characteristic functions are univariate functions of a quadratic form. The corresponding densities are easily found by means of the Hankel transform. Relations between spherical invariance and normality are discussed. Properties relating to the linear estimation problem are given.