An Introduction to Conditional Expectations and Stationarity
Rui Manuel de Almeida
Faculdade de Economia, Universidade de Coimbra
After a short review of properties of the Lebesgue integral, the equivalence between the problems of least squares prediction and the one concerning orthogonal projections on a closed subspace of a given Hilbert space is referred.
Conditional expectations are then present as a particular kind of projections on montone sequences of closed subspaces of L2, the World decomposition is mentioned.
Finally a brief reference to the interplay between stationary and ergodicity of the shift transformation is made.