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Grupo de Estudos Monetários e Financeiros

Estudos do GEMF, N.º 07 de 1997


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.

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