Prediction Theory Over Discrete Abelian Groups
D. M. Eaves · Transactions of the American Mathematical Society · 1969
Introduction.Classical least squares linear prediction theory is concerned with a stationary stochastic process (SSP); that is, with a family X(n) (n = 0, 1, -1,...) of complex-valued random variables on a probability space (Q, P), that have zero means, Gaussian joint distributions, and finite covariances (,X(ri), X(m)} depending only on n -m.One accomplishment of the theory is an analytical characterization of those SSPs for which some X(n) differs from its conditional expectation relative to those X(m) with m 0 be a finite regular Borel measure in the unit circle G; let dp/do be the Radon-Nikodym derivative of its absolutely continuous part relative to Lebesgue measure a in G;for each k let Pk be the orthogonal projection of L2(/i) onto the closed span of all \m with m^k.Then for all n, the norm being that in L2(p).